Topic
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.
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30 Mar 2011
TL;DR: In this paper, the generalized inflection points of the invertible sheaf were studied for linear systems with an integer a ≥ 1, where the inflection point is defined as a generalized point of a smooth curve C of genus g.
Abstract: Let E be a very general effective divisor of degree d on a smooth curve C of genus g. We study inflection points on linear systems |aE | for an integer a ≥ 1. They are called generalized inflection points of the invertible sheaf \({\mathcal{O}_C(E)}\). In case \({P
otin E}\) is a generalized inflection point of \({\mathcal{O}_C(E)}\) then it is a normal generalized inflection point. In case \({P\in E}\) then P has minimal vanishing sequences for E.
TL;DR: In this article, it was shown that the canonical Calabi-Yau triangulation is basepoint-free for a quasi-polarized canonical CCA for the case that the morphism is not birational onto its image.
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TL;DR: In this article, the Weierstrass semigroup was investigated at the ramification point at the intersection multiplicity point of the tangent line of the reduced divisor.
Abstract: Let $\varphi:\Sigma_1\longrightarrow \mathbb{P}^2$ be a blow up at a point on $\mathbb{P}^2$. Let $C$ be the proper transform of a smooth plane curve of degree $d\geq 4$ by $\varphi$, and let $P$ be a point on $C$. Let $\pi:\tilde{C}\longrightarrow C$ be a double covering branched along the reduced divisor on $C$ obtained as the intersection of $C$ and a reduced divisor in $|-2K_{\Sigma_1}|$ containing $P$. In this paper, we investigate the Weierstrass semigroup $H(\tilde{P})$ at the ramification point $\tilde{P}$ of $\pi$ over $P$, in the case where the intersection multiplicity at $\varphi(P)$ of $\varphi(C)$ and the tangent line at $\varphi(P)$ of $\varphi(C)$ is $d-1$.
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TL;DR: In this paper, the authors studied the class of projective algebraic surfaces X over C with a finite polyhedral Mori cone NE(X) subset NS(X), and showed that the class FPMC is bounded.
Abstract: We denote by FPMC the class of all non-singular projective algebraic surfaces X over C with a finite polyhedral Mori cone NE(X)\subset NS(X)\otimes R. If rho(X)=rk NS(X)\ge 3, then the set Exc(X) of all exceptional curves on X\in FPMC is finite and generates NE(X). Let \delta_E(X) be the maximum of (-E^2) and p_E(X) the maximum of p_a(E) respectively for E\in Exc(X). For fixed \rho \ge 3, \delta_E and p_E we denote by FPMC_{\rho,\delta_E,p_E} the class of all X\in FPMC such that \rho(X)=\rho, \delta_E(X)=\delta_E and p_E(X)=p_E. We prove that the class FPMC_{\rho,\delta_E,p_E} is bounded: for any X\in FPMC_{\rho,\delta_E,p_E} there exist an ample effective divisor h and a very ample divisor h' such that h^2\le N(\rho,\delta_E) and {h'}^2\le N'(\rho,\delta_E,p_E) where the constants N(\rho,\delta_E)$ and N'(\rho,\delta_E,p_E) depend only on (\rho, \delta_E) and (\rho, \delta_E, p_E) respectively.
One can consider Theory of surfaces X\in FPMC as Algebraic Geometry analog of the Theory of arithmetic reflection groups in hyperbolic spaces.
Patent•
09 Nov 2015
TL;DR: In this paper, an arithmetic device generates a quotient X/Y with respect to a divisor Y(i is an integer of 1 or more) as one element of a progression Y that can be regarded as an arithmetic progression.
Abstract: PROBLEM TO BE SOLVED: To reduce the number of calculations in division when a dividend can be regarded as a fixed value and a divisor as an arithmetic progression.SOLUTION: An arithmetic device generates a quotient X/Ywith respect to a divisor Y(i is an integer of 1 or more) as one element of a progression Y that can be regarded as an arithmetic progression, to generate an approximation value Zof the quotient X/Y. When two quotients including a quotient X/Yand a quotient X/Y(k