Stringy E-functions of hypersurfaces and of Brieskorn singularities
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Jan Schepers
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-Noguès, 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.
© de Gruyter 2009
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
Articles in the same Issue
- Tropical invariants from the secondary fan
- Quotients of projective spaces and spheres
- Gauss curvature flow on surfaces of revolution
- Stringy E-functions of hypersurfaces and of Brieskorn singularities
- Relations for virtual fundamental classes of Hilbert schemes of curves on surfaces
- The classification of surfaces with pg = q = 1 isogenous to a product of curves
- Some quasihomogeneous Legendrian varieties
- Families of surfaces and conjugate curve congruences
