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arXiv · 2607.19184

A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers

Matthew Satriano·Jeremy Usatine
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Abstract

Batyrev's conjecture on the non-negativity of stringy Hodge numbers has been a fundamental open problem, guiding and motivating many beautiful mathematical results in motivic integration, mirror symmetry, and the McKay correspondence. Let $M_0$ be the coarse moduli space of rank 2 semistable bundles with trivial determinant over a fixed smooth projective genus 3 curve. Using a formula, obtained by Kiem and Kiem-Li, for the stringy $E$-function of $M_0$, we verify that $M_0 \times\mathbb{P}^1$ is a counter-example to Batyrev's conjecture.

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Matthew Satriano, Jeremy Usatine. 2026-07-21. A counter-example to Batyrev's conjecture on the non-negativity of stringy Hodge numbers. https://arxiv.org/abs/2607.19184

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