Title: Stringy E-functions of hypersurfaces and of Brieskorn singularities
Authors: Schepers, Jan * ×
Veys, Willem * #
Issue Date: May-2009
Publisher: Walter de gruyter & co
Series Title: Advances in geometry vol:9 issue:2 pages:199-217
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.
ISSN: 1615-715X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
* (joint) first author
× corresponding author
# (joint) last author

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