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.

Class Group Relations in a Function Field Analogue of ${\mathbb Q}(\zeta_p, \sqrt[p]{n})$

Abstract: For an odd prime $p$ and polynomial $P(T)$, we consider the extension $F$ of $k={\mathbb F}_p(T)$ defined by adjoining a root of $x^p+Tx-P(T)$. Such a field is a function field analogue of the number field ${\mathbb Q}(\sqrt[p]{n})$. We prove two theorems about the Galois closure $L$ of $F$: that its degree-0 divisor class group is $A^{p-1}$ for some group $A$, and that its class number is the $(p-1)$-st power of the class number of $F$, in analogy with results of R. Schoof and T. Honda for number fields.

A note on the ampleness of numerically positive log canonical and anti-log canonical divisors

Abstract: In this short note, we consider the conjecture that the log canonical divisor (resp. the anti-log canonical divisor) $K_X + \Delta$ (resp. $-(K_X + \Delta)$) on a pair $(X, \Delta)$ consisting of a complex projective manifold $X$ and a reduced simply normal crossing divisor $\Delta$ on $X$ is ample if it is numerically positive. More precisely, we prove the conjecture for $K_X + \Delta$ with $\Delta eq 0$ in dimension 4 and for $-(K_X + \Delta)$ with $\Delta eq 0$ in dimension 3 or 4.

Method and device for conducting division in data processor

Abstract: PURPOSE: To realize an integer/floating point division operation through the use of a single correction SRT divider in a data processor. CONSTITUTION: Floating point/integer division is executed on a normalized plus mantissa (a dividend and a divisor) by using SRT division. Integer division shares a part of a floating point circuit and the sequence of the operation is changed during an integer division operation. The SRT divider 30 executes a series of operations before and behind a repetitive loop and reconstructs the integer/divisor and the dividend for the expression of a data route that an SRT algorithm requests to the mantissa of a floating point. During a repetitive loop, a quotient bit is selected and it is used for generating an intermediate partial remainder. The quotient bit is inputted to a quotient register for accumulating a final quotient mantissa. A mantissa full adder is used for generating the final remainder.

A note on Iitaka's conjecture $C_{3,1}$ in positive characteristics

Abstract: Let $f:X\to Y$ be a fibration from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ of characteristic $p >5$. We prove that if the generic fiber $X_{\eta}$ has big canonical divisor $K_{X_{\eta}}$, then $$\kappa(X)\ge\kappa(Y) + \kappa(X_{\eta}).$$

On the cyclotomic dedekind embedding and the cyclic Wedderburn embedding

Abstract: Let n≥1 and let p be a prime Expand j∈[0,p n −1]\(p) p-adically as j=∑ s≥0 a s p s with a s ∈[0,p−1] The #([0,j]\(p))th Z (p)[ζ p n ]-linear elementary divisor of the cyclotomic Dedekind embedding $$Z_{(p)} [\zeta _p ^n ] \otimes _{Z_{(p)} } Z_{(p)} [\zeta _p ^n ] \to \prod\limits_{i \in \left( {z/p_{}^n } \right)^* } {Z_{(p)} } [\zeta _p ^n ]$$ has valuation $$ - 1 + \sum\limits_{s \geqslant 0} {(a_s (s + 1) - a_{s + 1} (s + 2))} p^s $$ at 1−ζ p n There is a similar result for the related cyclic Wedderburn embedding