Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Tuesday, 11 March, 16:00–17:00, room TBA

Jan Schepers: Stringy Hodge numbers for a class of strictly canonical nondegenerate singularities

Abstract:

Abstract: In 1997, Batyrev defined the stringy E-function for complex algebraic varieties with Gorenstein canonical singularities. If the variety Y is projective and if the stringy E-function is a polynomial, then Batyrev defined the stringy Hodge numbers of Y, essentially as the coefficients of this polynomial. They satisfy analogous properties as usual Hodge numbers of smooth projective varieties and coincide with them for smooth Y. However, for singular Y it is from the definition not at all clear that they are nonnegative. This was conjectured by Batyrev. In this talk we first explain how to obtain the stringy E-function of a hypersurface from the motivic zeta function of Denef and Loeser. Then we describe a concrete class of strictly canonical nondegenerate hypersurface singularities that give rise to a polynomial stringy E-function. Moreover, we prove that Batyrev's conjecture is true for projective varieties with such singularities. The proof uses combinatorics of lattice polytopes.