Stringy E-functions of varieties with A-D-E singularities

Details Stringy E-functions of varieties with A-D-E singularities Stringy E-functions of varieties with A-D-E singularities

2005-11-14

arxiv.org/abs/math/0511348v2

Mathematics

Algebraic Geometry

29 pages, 8 figures and 5 tables, to appear in Manuscripta Math

Scientific paper

The stringy E-function for normal irreducible complex varieties with at worst log terminal singularities was introduced by Batyrev. It is defined by data from a log resolution. If the variety is projective and Gorenstein and the stringy E-function is a polynomial, Batyrev also defined the stringy Hodge numbers as a generalization of the Hodge numbers of nonsingular projective varieties, and conjectured that they are nonnegative. We compute explicit formulae for the contribution of an A-D-E singularity to the stringy E-function in arbitrary dimension. With these results we can say when the stringy E-function of a variety with such singularities is a polynomial and in that case we prove that the stringy Hodge numbers are nonnegative.

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