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摘要翻译：
我们证明了对于一个超曲面，Batyrev的弦E-函数可以看作是Hodge zeta函数的一个剩余，是Denef和Loeser的motivic zeta函数的一个特化。这是附加反演的一个很好的应用。如果仿射超曲面是由一个关于它的牛顿多面体的非退化的多项式给出的，那么从这个牛顿多面体可以计算出motivic zeta函数，从而可以计算出弦E-函数（由Artal、Cassou-Nogues、Luengo和Melle基于Denef和Hoornaert算法的工作）。我们用这个过程得到了一个简单的方法来计算一个Brieskorn奇点对弦E函数的贡献。作为推论，我们证明了具有一类严格规范Brieskorn奇点的类的stringy Hodge数是非负的。我们通过计算一个有趣的6维例子得出结论。证明了前文所得到的一个结论，即在低维情况下stringy Hodge数的非负性，在高维情况下是不成立的。
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英文标题：
《Stringy E-functions of hypersurfaces and of Brieskorn singularities》
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作者：
J. Schepers, W. Veys
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最新提交年份：
2007
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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 show that for a hypersurface Batyrev's stringy E-function can be seen as a residue of the Hodge zeta function, a specialization of the motivic zeta function of Denef and Loeser. This is a nice application of inversion of adjunction. If an affine hypersurface is given by a polynomial that is non-degenerate with respect to its Newton polyhedron, then the motivic zeta function and thus the stringy E-function can be computed from this Newton polyhedron (by work of Artal, Cassou-Nogues, Luengo and Melle based on an algorithm of Denef and Hoornaert). We use this procedure to obtain an easy way to compute the contribution of a Brieskorn singularity to the stringy E-function. As a corollary, we prove that stringy Hodge numbers of varieties with a certain class of strictly canonical Brieskorn singularities are nonnegative. We conclude by computing an interesting 6-dimensional example. It shows that a result, implying nonnegativity of stringy Hodge numbers in lower dimensional cases, obtained in our previous paper, is not true in higher dimension.
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PDF链接：
https://arxiv.org/pdf/0706.0798
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