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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TL;DR: The notion of a complete proof for simultaneousPositivity is developed and it is shown that under certain natural conditions, proofs for the simultaneous positivity of m forms will always require m steps.
81 citations
TL;DR: This work confirms a conjecture of Baker asserting that the rank of a divisor D on a (non-metric) graph is equal to theRank of D on the corresponding metric graph, and constructs an algorithm for computing therank of a Divisor on a tropical curve.
81 citations
TL;DR: In this paper, a simple alternative description of normal affine surfaces in terms of their graded rings as well as by defining equations is given. But this is based on a generalization of the Dolgachev-Pinkham-Demazure construction in the case of a hyperbolic grading.
Abstract: A classification of normal affine surfaces admitting a $\bf C^*$-action was given in the work of Bia{\l}ynicki-Birula, Fieseler and L. Kaup, Orlik and Wagreich, Rynes and others. We provide a simple alternative description of such surfaces in terms of their graded rings as well as by defining equations. This is based on a generalization of the Dolgachev-Pinkham-Demazure construction in the case of a hyperbolic grading. As an apllication we determine the structure of singularities, of the orbits and the divisor class groups for such surfaces.
80 citations
TL;DR: In this paper, the authors initiated the study of GCD matrices in the direction of their structure, determinant, and arithmetic in Z n. Several open problems are posed.
80 citations
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TL;DR: In this paper, the log canonical divisor of the ambient space with respect to a subvariety of codimension 2 was derived by using Knudsen's moduli space of pointed stable curves of genus 0.
Abstract: We obtain a formula which relates the log canonical divisor of the ambient space with that of a subvariety of codimension 2 by using Knudsen's moduli space of pointed stable curves of genus 0.
78 citations