Stringy E-functions of hypersurfaces and of Brieskorn singularities

J. Schepers; W. Veys

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arXiv · 0706.0798

Stringy E-functions of hypersurfaces and of Brieskorn singularities

J. Schepers·W. Veys

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Abstract

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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BibTeX RIS

J. Schepers, W. Veys. 2007-06-06. Stringy E-functions of hypersurfaces and of Brieskorn singularities. https://arxiv.org/abs/0706.0798

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