发表机构
University of Waterloo（滑铁卢大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究确定了Batyrev非负性猜想的维数阈值：其在维数≤4时成立，维数≥5时存在反例，为相关领域提供了关键结论。
AI 中文摘要
Batyrev非负性猜想是镜像对称、动机积分与McKay对应中的核心指导性猜想。我们证明该猜想在维数不超过4时成立，并给出了维数至少为5时的反例。
英文摘要
The stringy $E$-function is a fundamental invariant of varieties with log-terminal singularities, which was introduced by Batyrev as a singular analogue of the Hodge--Deligne polynomial. Its coefficients (up to an appropriate sign) are the stringy Hodge numbers $h_{\mathrm{str}}^{p,q}(Y)$. We completely determine when these coefficients are universally non-negative:~for each triple $(n,p,q)$, we classify when $h_{\mathrm{str}}^{p,q}(Y)\geq 0$ for every projective Gorenstein canonical $n$-fold $Y$; we answer this question both when we assume $E_{\mathrm{str}}(Y;u,v)$ is a polynomial and when we drop this condition. As a consequence, we settle Batyrev's non-negativity conjecture in all dimensions:~it holds in dimensions at most $4$ and fails in every dimension at least $5$.
