Showing papers on "Divisor published in 1999"

Hermitian-einstein metrics on parabolic stable bundles

Abstract: Let $$\overline M $$ be a compact complex manifold of complex dimension two with a smooth Kahler metric and D a smooth divisor on $$\overline M $$ . If E is a rank 2 holomorphic vector bundle on $$\overline M $$ with a stable parabolic structure along D, we prove the existence of a metric on $$E'{\text{ = }}E|_{\overline M \backslash D} $$ (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of the Kahler metric to $$\overline M $$ ĚD. A converse is also proved.

The Erdős–Ko–Rado Theorem for Integer Sequences

Abstract: , q, t we determine the maximum number of integer sequences \(\) which satisfy \(\) for \(\), and any two sequences agree in at least t positions. The result gives an affirmative answer to a conjecture of Frankl and Furedi.

On the divisor class group of double solids

Abstract: For a double solid V→ℙ3> branched over a surface B⊂ℙ3(ℂ) with only ordinary nodes as singularities, we give a set of generators of the divisor class group \(\) in terms of contact surfaces of B with only superisolated singularities in the nodes of B. As an application we give a condition when H* (˜V , ℤ) has no 2-torsion. All possible cases are listed if B is a quartic. Furthermore we give a new lower bound for the dimension of the code of B.

Existence of pencils with prescribed scrollar invariants of some general type

Abstract: Let C be an irreducible smooth projective non-hyperelliptic curve of genus g defined over the field C of complex numbers. Let g\ be a complete base-point free special linear system on C. The scrollar invariants of g\ are defined as follows. Let C be canonically embedded in P~ and let X be the union of the linear spans (D) with D e g\ . This defines a set of integers e\ > ... > ek-i > 0 such that X is the image of the projective bundle P(e\\... e^-i) = P(OPι (ei) Θ . . . Θ OPι (βk-i)) using the tautological bundle (see e.g. [2]; [7]). Those integers e ι ;e 2 ; . . . e^-i are called the scrollar invariants of g\. Those scrollar invariants determine (and are determined by) the complete linear systems associated to multiples of the linear system g\. For 1 i Here KC denotes a canonical divisor on C. Let m = βfc-ι+2. Then m is defined by the following conditions: dim(|(ra—l)p£|) — m—1 and dim(|ra ra. In case \mg\\ is birationally very ample then the scrollar invariants satisfy the inequalities e* '^'~^m 1 -f (x — (j — l)m + l) j . Equality (if not in conflict with the Riemann-Roch Theorem) can be expected being the most general case for a fixed value of m. The inequalities also imply dim(|(λ; — l)mg\.\) = dim(|((fc — l)ra 1)^ | ) 4k. This implies that \((k — l)m l)g\\ is not special. Using the dimension bound one obtains g < [(k k)m 2k + 2]/2. (This easy but interesting consequence from the inequalities is not mentioned by Kato and Ohbuchi.) In this paper we prove the following theorem.

Divisors on Principally Polarized Abelian Varieties

Abstract: The purpose of this paper is to show how generalizations of generic vanishing theorems to a ℚ -divisor setting can be used to study the geometric properties of pluritheta divisors on a principally polarized Abelian variety (PPAV for short).

Remainder calculating method, modular-multiplication method, remainder calculating apparatus, modular-multiplication apparatus and recording medium

Abstract: In a remainder calculating method and a modular-multiplication method on the basis of a Montgomery method, a number expressed by N (N=c2 d±1) is used as a divisor N. In order to calculate a remainder in the case of dividing a dividend Y by a divisor N on the basis of a Montgomery method, a number expressed by a condition of N=c2 d−1 is used as the divisor N, and the following steps are repeatedly carried out; the steps includes: a step of adding a product of a least digit value yo of the dividend Y and c to a lower d-bit position of the dividend Y; and a step of setting a portion excluding the least digit of the additive result as a next dividend.

The distribution of prime divisors in finitely generated domains

Abstract: In this paper we show that each divisor class of a finitely generated k-algebra R (k a field) contains a prime divisor if k is Hilbertian or if dim R≥ 2. On the way we also obtain partial results for domains finitely generated over an one-dimensional noetherian domain.

Method for achieving correctly rounded quotients in algorithms based on fused multiply-accumulate without requiring the intermediate calculation of a correctly rounded reciprocal

Abstract: A method and apparatus for performing a floating point division of a dividend (a) by a divisor (b) to produce a correctly rounded-to-nearest quotient (q′) having a mantissa of P bits in a data processing system is disclosed. In one embodiment, the data processing system computes a current quotient estimate (q m ′, where m represents an integer and m>=0) that is within 1 ulp of a true quotient (a/b). Then the data processing system computes a current remainder estimate (r m ′) based on the dividend (a), the divisor (b) and the current quotient estimate (q m ′). The data processing system also computes a current reciprocal estimate (y n ′, where n represents an integer and n>=0) based on a reciprocal intermediate value (E) with a relative error with respect to a true reciprocal of the divisor (1/b) of less than or equal to z/(2 2P ) (where z is an integer derived from error analyses of computations of the current reciprocal estimate (y n ′)). Finally, the data processing system obtains the correctly rounded-to-nearest quotient (q′), except possibly when z>=(2 P −M b ) (where M b represents mantissa of the divisor, b), based on the current remainder estimate (r m ′), the current reciprocal estimate (y n ′) and current quotient estimate (q m ′).

On the Q-divisor method and its application

Abstract: For smooth projective 3-folds of general type, we prove that the relative canonical stability $\mu_s(3)\leq 8$. This is induced from our improved result of Kollar: the m-canonical map of a smooth projective 3-fold of general type is birational whenever $m\geq 5k+6$, provided $P_k(X)\geq 2$. The Q-divisor method is intensively developed to prove our results.

Method and apparatus for calculating the remainder of a modulo division

Abstract: A non-iterative technique for calculating the remainder of modulo division, which requires significantly fewer operations than the traditional iterative technique for the same calculation. The number of calculations required in the present invention is independent of the number of bits of the divisor in the modulo operation. Two requirements of the non-iterative technique are that the value of the divisor D should be equal to 2 n −1 (where n is the number of bits of the divisor D) and the value of the dividend N should be less than or equal to (D−1) 2 , but greater than or equal to zero. If these two conditions are met, the remainder R of N mod D is determined by summing the upper n 2 and lower n 2 bits of the dividend N.

Split remainder divider

Abstract: The invention provides computer apparatus for performing a division operation having a dividend mathematically divided by a divisor. The dividend and the divisor are split between a state machine and an array of carry save adders. The most significant bits of the dividend and the divisor are input to the state machine and the least significant bits of the dividend and the divisor are input to the carry save adder array. The state machine is fully encoded with partial remainder values and quotient digit values for all possible combinations of the most significant bits of the divisor and the dividend. The carry save adders add the respective least significant bits of the dividend and the divisor and output spillover signals to the state machine. The state machine provides partial remainders and quotient digits selected from the encoded partial remainder values and quotient digit values dependent on (i.e. as a function of) the most significant bits of the dividend, divisor and the spillover signals.

Gigantic pairs of minimal clones

Abstract: L. Szabo (1992) asked for the minimal number n=n(|A|) such that the clone of all operations on A can be generated as the join of n minimal clones. He showed, e.g., n(p)=2 for any prime p, and later G. Czedli (1998) proved that if k has a divisor /spl ges/5 then n(k)=2. In this paper, a pair (f, g) of operations is called gigantic if each of f and g generates a minimal clone and the set {f, g} generates the clone of all operations. First, we give a general theorem to characterize a gigantic pair. Then we show that n(k)=2 for every k which is not a power of 2.

The Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface

Abstract: Given a compact Riemann surface $\bar{X}$ of genus $g$ and a point $q$ on $\bar{X}$, we consider $X:=\bar{X}\setminus\{q\}$ with a basepoint $p\in X$. The extension of mixed Hodge structures, given by the weights -1 and -2, of the mixed Hodge structure on the fundamental group (in the sense of Hain) is studied. We show that it naturally corresponds on the one hand to the element $(2g q-2 p-K)$ in $\Pic^0(\bar{X})$, where $K$ represents the canonical divisor, and on the other hand to the respective extension of $\bar{X}$. Finally, we prove a pointed Torelli theorem for punctured Riemann surfaces.

Stable maps and branch divisors

Abstract: We construct a natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisor contruction of Mumford from sheaves to complexes. The construction is valid in flat families. The generalized branch divisor of a stable map to a nonsingular curve X yields a canonical morphism from the space of stable maps to a symmetric product of X. This branch morphism (together with virtual localization) is used to compute the Hurwitz numbers of covers of P^1 for all genera and degrees in terms of Hodge integrals.

Restriction of stable rank two vector bundles in arbitrary characteristic

Abstract: Let $X$ be a smooth variety defined over an algebraically closed field of arbitrary characteristic and $\O_X(H)$ be a very ample line bundle on $X$. We show that for a semistable $X$-bundle $E$ of rank two, there exists an integer $m$ depending only on $\Delta(E).H^{\dim(X)-2}$ and $H^{\dim(X)}$ such that the restriction of $E$ to a general divisor in $|mH|$ is again semistable. As corollaries we obtain boundedness results, and weak versions of Bogomolov's theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic.

Connectivity of Circulant Graphs

Abstract: In this paper, an explicit expression is derived for the connectivity of a connected circulant graph whose connectivity is less than its point degree, that is k(G) = :m is a proper divisor of n and.

Method and apparatus for arithmetic operation and recording medium of method of operation

Abstract: An integer Z101 is divided by another integer I102 to determine the remainder R109 The integer I102 is expressed by a polynominal comprising powers of the basic unit of computer operation By limiting the divisor according to the basic unit of computer operation, no shift operation is required as opposed to the conventional method, and remainders can thus be determined simply by addition and subtraction This allows code size to be compact, resulting in high-speed determination of integer remainders

Method and device for accelerating data processing of calculator

Abstract: PROBLEM TO BE SOLVED: To accelerate data processing at a calculator using a Montgomery logarithm while using a processor for handling m-bit operand data. SOLUTION: Concerning an arbitrary divisor (n) being an input data, the calculation of Montgomery value defined as 2 mod (n) is performed, and data processing is accelerated by applying 2 mod (n) to the calculator. The value of 2 * is loaded to a first register, the divisor (n) is loaded to a second register, and the bit of the divisor (n) is shifted toward a most significant bit(MSB). Remainder calculating processing is performed by repeatedly subtracting the value of the second register from the value of the first register unit until the value of the first register is smaller than the value of input data (n). Multiplication processing of squaring the remainder of the calculation processed value of the first register for log2 (k) times is performed. While reducing the number of times of calculation required for the processor having a limited operand size, the Montgomery value is calculated concerning the arbitrary divisor and provided for the calculator.

Method and circuit for digital division

Abstract: A method and apparatus for calculating a quotient from a dividend and a divisor, wherein the divisor can be represented as (2N+2M) where N is greater than M, and wherein the dividend comprises an X-bit binary number divisible by the divisor without a remainder. The values of N and M for the dividend are determined such that the divisor is equal to the value (2N+2M). The M-th through the (N−1)-th bits of the dividend are selected as lower order bits of the quotient. The (N−1)-th and the (2N−M−1)-th bits of the dividend are examined. If the (N−1)-th bit of the dividend is “1” and if the (2N−M−1)-th bit of the dividend is “0”, then one is subtracted from a value represented by the (2N−M)-th through the (X−1)-th bits of the dividend to obtain a result as higher order bits of the quotient. Otherwise, the (2N−M)-th through the (X−1)-th bits of the dividend are selected as higher order bits of the quotient. Finally, the higher order bits and the lower order bits are concatenated to obtain the quotient.

Method for arithmetic operation and recording medium of method of operation

Abstract: An integer Z101 is divided by another integer I102 to determine the remainder R109 The integer I102 is expressed by a polynominal comprising powers of the basic unit of computer operation By limiting the divisor according to the basic unit of computer operation, no shift operation is required as opposed to the conventional method, and remainders can thus be determined simply by addition and subtraction This allows code size to be compact, resulting in high-speed determination of integer remainders

Asymptotic Formulae and Divisor Problems

Abstract: We investigate the asymptotic behaviour of the summatory functions of τz(n, θ), τk(n, θ) zω (n) and τk(n, θ) zΩ (n).

Reduction of points in the group of components

Abstract: Let $K$ be a complete discrete valuation field with ring of integers $\co_K$. Let $X/K$ be a proper smooth curve and let $A/K$ denote its jacobian. Let $P$ and $Q$ belong to $X(K)$. The divisor $P - Q$ defines a $K$-rational point of $A/K$. In this article, we study the reduction of $P - Q$ in the Neron model ${\cal A}_K/{\cal O}_K$ of $A/K$ in terms of the reductions of the points $P$ and $Q$ in a regular model $\cx/\co_K$ of $X/K$. The author introduced earlier two functorial filtrations of the prime-to-$p$ part of the group of component $\Phi_K$ of ${\cal A}_K/{\cal O}_K$. Filtrations for the full group $\Phi_K$ were later introduced by Bosch and Xarles. Given two points $P$ and $Q$ in $X(K)$, it is natural to wonder whether it is possible to predict when the reduction of $P-Q$ in $\Phi_K$ belongs to one of these functorial subgroups. We give in this paper a sufficient condition on the special fiber of a model $\cx$ for the image of $P-Q$ in $\Phi_K$ to belong to the subgroup $\Psi_{K,L}$. When this condition is satisfied, we are able to provide a formula for the order of this image. We conjecture that the sufficient condition alluded to above is also necessary and we provide evidence in support of this conjecture. We also discuss cases where the image of $P-Q$ belongs to a functorial subgroup of $\Psi_{K,L}$, using a pairing associated to $\Phi_K$.

Even Sets of Lines on Quartic Surfaces

Abstract: An effective divisor D on a smooth (compact complex) surface X is called even, if its class $[D] \in H^2(X,\Z)$ is divisible by 2. D may be assumed reduced w.l.o.g. Then D being even is equivalent to the existence of a double cover $Y \to X$ branched exactly over D. The aim of this note is to study arrangements of $n \leq 10$ distinct lines on a smooth quartic surface $X \subset \P_3$, which form an even divisor in this sense. The result is that for $n \leq 8$ there are no unexpected ones (one type of six lines, four types of eight lines). And for n=10 a partial classification is given in the following sense: Each even set of ten lines on a smooth quartic surface is of one of eleven different types. At the moment I do not know which of these types do actually occur. The proof for these facts is messy, essentially checking cases.

Division circuit and partial divider used for the same

Abstract: PROBLEM TO BE SOLVED: To provide a division circuit which operates at high speed and which can simultaneously find a quotient and a remainder. SOLUTION: A dividend is inputted to the partial divider 2-1 and a partial quotient and the partial remainder of the dividend against the divisor are calculated. The obtained partial divisor is inputted to the partial divider 2-2 of a next stage and the partial quotient and the partial remainder of the partial remainder in the former stage against the dividend are calculated. Then, it is repeated until the partial remainder becomes smaller than the divisor. The total of all the obtained partial quotients is outputted from an adder 5 and it is set to be the quotient. The partial remainder 3-s obtained in the partial divider 2-s in the final stage becomes the remainder.

Nonsymmetric problem of divisors in an arithmetic progression

Abstract: We investigate the distribution of values of a nonsymmetric divisor functiond(a,b; n) in an arithmetic progression with increasing difference.

Decoding Algebraic Geometry codes by a key equation

Abstract: A new effective decoding algorithm is presented for arbitrary algebraic-geometric codes on the basis of solving a generalized key equation with the majority coset scheme of Duursma. It is an improvement of Ehrhard's algorithm, since the method corrects up to the half of the Goppa distance with complexity order O(n**2.81), and with no further assumption on the degree of the divisor G.

Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve

Abstract: Let $X$ be a compact connected Riemann surface of genus $g$, with $g\geq 2$, and ${\cal M}_{\xi}$ a smooth moduli space of fixed determinant semistable vector bundles of rank $n$, with $n\geq 2$, over $X$. Take a smooth anticanonical divisor $D$ on ${\cal M}_{\xi}$. So $D$ is a Calabi-Yau variety. We compute the number of moduli of $D$, namely $\dim H^1(D, T_D)$, to be $3g-4 + \dim H^0({\cal M}_{\xi}, K^{-1}_{{\cal M}_{\xi}})$. Denote by $\cal N$ the moduli space of all such pairs $(X',D')$, namely $D'$ is a smooth anticanonical divisor on a smooth moduli space of semistable vector bundles over the Riemann surface $X'$. It turns out that the Kodaira-Spencer map from the tangent space to $\cal N$, at the point represented by the pair $(X,D)$, to $H^1(D, T_D)$ is an isomorphism. This is proved under the assumption that if $g =2$, then $n eq 2,3$, and if $g=3$, then $n eq 2$.

Holomorphic Curves and Integral Points off Divisors

Abstract: We deal with the distributions of holomorphic curves and integral points off divisors. We will simultaneouly prove an optimal dimension estimate from above of a subvariety W off a divisor D which contains a Zariski dense entire holomorphic curve, or a Zariski dense D-integral point set, provided that in the latter case everything is defined over a number field. Then, if the number of components of D is large, the estimate leads to the constancy of such a holomorphic curve or the finiteness of such an integral point set. At the begining, we extend logarithmic Bloch-Ochiai's Theorem to the Kaehler case.