Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.

Crepant resolutions of double covers: On the Cynk-Hulek criterion for crepant resolutions of double cover

Abstract: A collection $S = \{D_1,\ldots, D_n\}$ of divisors in a smooth variety $X$ is an {\em arrangement} if intersections of all subsets of $S$ are smooth We show that a double cover of $X$ ramified on an arrangement has a crepant resolution under additional hypotheses Namely, we assume that all intersection components that change the canonical divisor when blown up satisfy are {\em splayed}, a property of the tangent spaces of the components first studied by Faber This strengthens a result of Cynk and Hulek, which requires a stronger hypothesis on the intersection components Further, we study the singular subscheme of the union of the divisors in $S$ and prove that it has a primary decomposition where the primary components are supported on exactly the subvarieties which are blown up in the course of constructing the crepant resolution of the double cover

Non-restoring division device

Abstract: PURPOSE: To execute division at high speed by providing an addition/subtraction circuit adding/subtracting a dividend and a divisor and a judgement register judging the positive/negative of the result of addition/subtraction and supplying a judged result to a dividend storage register and a second divisor selection circuit as a selection signal. CONSTITUTION: The dividend storage register 1 stores dividend data and divisor storage registers 2, 3 and 4 store onefold, twofold and threefold data of the divisor. A control circuit 5 generates control signals selecting onefold, twofold and threefold data of divisor data. A first divisor selection circuit 6 selects onefold, twofold and threefold divisor data of the divisor. The addition/ subtraction circuit 7 adds/subtracts the dividend and the divisor, and an operation result storage register 8 stores an addition/subtraction result. A quotient generation circuit 9 generates a part of the quotient and a quotient storage register 10 stores the quotient by division. A quotient subtraction circuit 11 subtracts the quotient which is stored when a subtraction result is negative. A judgement register 12 stores the judgement signal of positive/negative information.

Semistability of Rational Principal $GL_n$-Bundles in Positive Characteristic

Abstract: Let $k$ be an algebraically closed field of characteristic $p>0$, $X$ a smooth projective variety over $k$ with a fixed ample divisor $H$. Let $E$ be a rational $GL_n(k)$-bundle on $X$, and $\rho:GL_n(k)\rightarrow GL_m(k)$ a rational $GL_n(k)$-representation at most degree $d$ such that $\rho$ maps the radical $R(GL_n(k))$ of $GL_n(k)$ into the radical $R(GL_m(k))$ of $GL_m(k)$. We show that if $F_X^{N*}(E)$ is semistable for some integer $N\geq\max\limits_{0

On odd deficient-perfect numbers with four distinct prime divisors

Abstract: For a positive integer $n$, let $\sigma(n)$ denote the sum of the positive divisors of $n$. Let $d$ be a proper divisor of $n$. We call $n$ a deficient-perfect number if $\sigma(n)=2n-d$. In this paper, we show that the only odd deficient-perfect number with four distinct prime divisors is $3^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2}$.