Stringy E-functions of varieties with A-D-E singularities |
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Authors: | Jan Schepers |
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Institution: | (1) Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium |
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Abstract: | 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.
Research Assistant of the Fund for Scientific Research - Flanders (Belgium) (F.W.O.), |
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Keywords: | |
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