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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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Journal ArticleDOI
TL;DR: An automorphism σ of order (a divisor of)n of the groupG is called n-splitting if\(gg^\sigma \cdots gg^{n - 1} } = 1\) for everyg∈G.
Abstract: An automorphism σ of order (a divisor of)n of the groupG is calledn-splitting if\(gg^\sigma \cdots gg^{\sigma ^{n - 1} } = 1\) for everyg∈G.
Posted Content
TL;DR: In this article, the authors consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties.
Abstract: In this note we consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties. In particular we show that there is such a D with h^1(X,D) > 0 and h^1(X,2D) = 0.
Book ChapterDOI
01 Jan 2019
TL;DR: In this paper, a sequence of approximations of the reciprocal of the divisor b, derived by the Newton-Raphson method, are used for multiplicative division.
Abstract: Multiplicative division algorithms are typically based on a sequence of approximations of the reciprocal of the divisor b, derived by the Newton-Raphson method.
Journal ArticleDOI
Ryo Takahashi1
TL;DR: In this article, the interior, closure and boundary, and convex polyhedral subcones of a commutative noetherian ring were studied and various equivalent conditions for R to have only finitely many rank r maximal Cohen-Macaulay points.
Abstract: Let R be a commutative noetherian ring. Let $$\mathsf {H}(R)$$ be the quotient of the Grothendieck group of finitely generated R-modules by the subgroup generated by pseudo-zero modules. Suppose that the $$\mathbb {R}$$ -vector space $$\mathsf {H}(R)_\mathbb {R}=\mathsf {H}(R)\otimes _\mathbb {Z}\mathbb {R}$$ has finite dimension. Let $$\mathsf {C}(R)$$ (resp. $$\mathsf {C}_r(R)$$ ) be the convex cone in $$\mathsf {H}(R)_\mathbb {R}$$ spanned by maximal Cohen–Macaulay R-modules (resp. maximal Cohen–Macaulay R-modules of rank r). We explore the interior, closure and boundary, and convex polyhedral subcones of $$\mathsf {C}(R)$$ . We provide various equivalent conditions for R to have only finitely many rank r maximal Cohen–Macaulay points in $$\mathsf {C}_r(R)$$ in terms of topological properties of $$\mathsf {C}_r(R)$$ . Finally, we consider maximal Cohen–Macaulay modules of rank one as elements of the divisor class group $${\text {Cl}}(R)$$ .
Journal ArticleDOI
TL;DR: In this paper, the authors compare the local topological obstruction theory with the geometric obstruction theory (i.e., the obstruction to the deformation of $D$ as an effective Cartier divisor of a first order infinitesimal deformations of $X$), and apply this to study the jumping locus of families of linear systems and the Noether-Lefschetz locus.
Abstract: Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is well-known that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in $H^2(\mathcal{O}_X)$. In this article, we replace $H^2(\mathcal{O}_X)$ by $H^2_D(\mathcal{O}_X)$ and give an analogous topological obstruction theory. We compare the resulting local topological obstruction theory with the geometric obstruction theory (i.e., the obstruction to the deformation of $D$ as an effective Cartier divisor of a first order infinitesimal deformations of $X$). We apply this to study the jumping locus of families of linear systems and the Noether-Lefschetz locus. Finally, we give examples of first order deformations $X_t$ of $X$ for which the cohomology class $[D]$ deforms as a Hodge class but $D$ does not lift as an effective Cartier divisor of $X_t$.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021157
2020172
2019127
2018120
2017140