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

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.

Disclosure

“A COUNTER-EXAMPLE TO BATYREV’S CONJECTURE 3 We present the following counter-example to Conjecture 1.1, which was discov- ered with the assistance of ChatGPT. Theorem 1.2. Let C be a smooth complex projective curve of genus 3 and let M0 be the coarse moduli space of rank 2 semistable bundles over C with trivial determinant. Then X = M0 × P 1 is a 7-dimension”

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Classification

Substantial mathematical content or result generation

Multiplier

10

Verified

2026-08-23T19:00:46.274768Z

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