On the nonnegativity of stringy Hodge numbers

TL;DR

This paper investigates the nonnegativity of stringy Hodge numbers in algebraic geometry, proving new results for threefolds and fourfolds, and confirming Batyrev's conjecture in specific cases using advanced mathematical tools.

Contribution

It proves the nonnegativity of (p,1)-stringy Hodge numbers and verifies Batyrev's conjecture for certain fourfolds, advancing understanding of stringy invariants.

Findings

(p,1)-stringy Hodge numbers are nonnegative

New results on the stringy Hodge diamond for threefolds

Batyrev's conjecture holds for some fourfolds

Abstract

We study the nonnegativity of stringy Hodge numbers of a projective variety with Gorenstein canonical singularities, which was conjectured by Batyrev. We prove that the $(p,1)$-stringy Hodge numbers are nonnegative, and for threefolds we obtain new results about the stringy Hodge diamond, which hold even when the stringy $E$-function is not a polynomial. We also use the Decomposition Theorem and mixed Hodge theory to prove Batyrev's conjecture for a class of fourfolds.