摘要翻译:
本文的目的是给出热带几何的一个基本定理的构造性证明:给定热带簇上的一个点(用初始理想定义),在代数簇中该点存在一个Puiseux值的“提升”。这个定理之所以如此基本,是因为它证明了为什么一个热带变体(用初始理想组合定义)携带关于代数变体的信息:它是一个代数变体在估价图下的Puiseux级数上的图像。当基域为有理数时,我们用奇异值和Gfan实现了“提升算法”。作为副产品,我们得到了一个计算(k^{n+1},0)空间曲线奇点的Puiseux展开式的算法。
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英文标题:
《An algorithm for lifting points in a tropical variety》
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作者:
Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig
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最新提交年份:
2009
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Commutative Algebra 交换代数
分类描述:Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环,模,理想,同调代数,计算方面,不变理论,与代数几何和组合学的联系
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英文摘要:
The aim of this paper is to give a constructive proof of one of the basic theorems of tropical geometry: given a point on a tropical variety (defined using initial ideals), there exists a Puiseux-valued ``lift'' of this point in the algebraic variety. This theorem is so fundamental because it justifies why a tropical variety (defined combinatorially using initial ideals) carries information about algebraic varieties: it is the image of an algebraic variety over the Puiseux series under the valuation map. We have implemented the ``lifting algorithm'' using Singular and Gfan if the base field are the rational numbers. As a byproduct we get an algorithm to compute the Puiseux expansion of a space curve singularity in (K^{n+1},0).
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PDF链接:
https://arxiv.org/pdf/0705.2441