Stringy Invariants of Algebraic Varieties and Lattice Polytopes

Abstract

We present topological invariants in the singular setting for projective ℚ-Gorenstein varieties with at worst log-terminal singularities, such as stringy Euler numbers, stringy Chern classes, stringy Hodge numbers, and stringy E-functions. In the toric setting, we give formulae to efficiently compute these stringy invariants. Using these combinatorial expressions and the stringy Libgober-Wood identity, we derive several appealing new combinatorial identities for lattice polytopes. We go on to generalise the famous ‘number 12’ and ‘number 24’ identities which hold far more generally than previously expected.