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摘要翻译：
我们通过一个有限的单项式值序列定义了与一个多环或解析不可约的拟普通超曲面奇点(S，0)相关的Poincar E级数，使得其中至少有一个以原点0为中心。这涉及到一个多分次环的定义，这个多分次环与奇异性的解析代数相关联。我们证明了Poincar级数是一个整数系数有理函数，它也可以定义为关于由值定义的函数的奇异性的解析代数的投影上的关于Euler特性的积分。特别地，在奇异轨迹上和点0上，与本质因子相关的除法值集相关的Poincar级数是奇异点的解析不变量。在拟普通超曲面情形下，我们证明了该Poincar E级数是由特征单点的归一化序列决定的，并且它是由特征单点的归一化序列决定的。在解析情形中，这些单项式定义了超曲面奇点的嵌入拓扑类型的完全不变量。
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英文标题：
《Quasi Ordinary Singularities, Essential Divisors and Poincare Series》
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作者：
Pedro Daniel Gonzalez Perez, Fernando Hernando
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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 define Poincar\'e series associated to a toric or analytically irreducible quasi-ordinary hypersurface singularity, (S,0), by a finite sequence of monomial valuations, such that at least one of them is centered at the origin 0. This involves the definition of a multi-graded ring associated to the analytic algebra of the singularity by the sequence of valuations. We prove that the Poincar\'e series is a rational function with integer coefficients, which can be defined also as an integral with respect of the Euler characteristic, over the projectivization of the analytic algebra of the singularity, of a function defined by the valuations. In particular, the Poincar\'e series associated to the set of divisorial valuations associated to the essential divisors, considered both over the singular locus and over the point 0, is an analytic invariant of the singularity. In the quasi-ordinary hypersurface case we prove that this Poincar\'e series determines and it is determined by the normalized sequence of characteristic monomials. These monomials in the analytic case define a complete invariant of the embedded topological type of the hypersurface singularity.
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PDF链接：
https://arxiv.org/pdf/0705.0603
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