摘要翻译:
本文给出了关于剪接商奇点的几个结果:所有自然线丛的第一上同调维数的组合表达式,关于线丛相对截面维数的等变Campillo-Delgado-Gusein-Zade型公式(证明了等变的、除数的多元Hilbert级数是拓扑的),解析函数芽的因子的组合描述,以及由分解图给出的奇点重数的表达式。另外,我们建立了任意有理同调球奇点链的Seiberg-Witten不变量的一个新公式。
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英文标题:
《The cohomology of line bundles of splice-quotient singularities》
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作者:
Andr\'as N\'emethi
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最新提交年份:
2008
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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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英文摘要:
We provide several results on splice-quotient singularities: a combinatorial expression of the dimension of the first cohomology of all `natural' line bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the dimension of relative sections of line bundles (proving that the equivariant, divisorial multi-variable Hilbert series is topological), a combinatorial description of divisors of analytic function-germs, and an expression for the multiplicity of the singularity from its resolution graph. Additional, we establish a new formula for the Seiberg-Witten invariants of any rational homology sphere singularity link.
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PDF链接:
https://arxiv.org/pdf/0810.4129