AI 中文总结
该研究针对巴蒂列夫关于弦霍奇数非负性的猜想，借助ChatGPT给出反例，此猜想在多个数学领域意义重大，此次发现为相关研究带来新情况。
AI 中文摘要
巴蒂列夫关于弦霍奇数非负性的猜想一直是一个基本的开放性问题，在动机积分、镜像对称和麦凯对应中引导并激发了许多优美的数学成果。我们借助OpenAI的ChatGPT给出了一个巴蒂列夫猜想的反例。
英文摘要
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.
