Stringy Hodge numbers of strictly canonical nondegenerate singularities

Abstract

We describe a class of isolated nondegenerate hypersurface singularities that give a polynomial contribution to Batyrev’s stringy E 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.