Stringy Hodge numbers of strictly canonical nondegenerate singularities

Schepers, Jan

doi:10.1090/S1056-3911-2011-00546-8

Author: Jan Schepers
Journal: J. Algebraic Geom. 21 (2012), 273-297
DOI: https://doi.org/10.1090/S1056-3911-2011-00546-8
Published electronically: March 28, 2011
MathSciNet review: 2877435
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Abstract | References | Additional Information

Abstract: We describe a class of isolated nondegenerate hypersurface singularities that give a polynomial contribution to Batyrev’s stringy $E$-function. These singularities are obtained by imposing a natural condition on the facets of the Newton polyhedron, and they are strictly canonical. We prove that Batyrev’s conjecture concerning the nonnegativity of stringy Hodge numbers is true for complete varieties with such singularities, under some additional hypotheses on the defining polynomials (e.g. convenient or weighted homogeneous). The proof uses combinatorics on lattice polytopes. The results form a strong generalisation of previously obtained results for Brieskorn singularities.

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Additional Information

Jan Schepers
Affiliation: K.U.Leuven, Department of Mathematics, Celestijnenlaan 200B, B-3001 Leuven, Belgium
Email: janschepers1@gmail.com

Received by editor(s): April 30, 2009
Received by editor(s) in revised form: August 28, 2009
Published electronically: March 28, 2011
Additional Notes: Supported by VICI grant 639.033.402 from the Netherlands Organisation for Scientific Research (NWO). During the completion of this paper, the author was a Postdoctoral Fellow of the Research Foundation - Flanders (FWO). Part of this work was carried out during a stay at the Institut des Hautes Études Scientifiques (IHÉS). I am very grateful that I was given the opportunity to work there.
Dedicated: Dedicated to Joost van Hamel