关于非正则霍奇数在crepant双有理等价下的不变性
On the invariance of irregular Hodge numbers under crepant birational equivalences
- Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究朗道 - 金兹堡模型\((U,f)\)中扭曲德拉姆上同调\(\mathrm{H}^k_{\mathrm{dR}}(U,f)\)的非正则霍奇数，证明其在crepant双有理等价下不变，类似巴蒂列夫 - 孔采维奇定理对卡拉比 - 丘流形霍奇数的结论。
AI中文摘要：
巴蒂列夫 - 孔采维奇定理表明双有理卡拉比 - 丘流形具有相同的霍奇数。本文证明了对于由光滑拟射影复流形\(U\)及其正则函数\(f\)组成的朗道 - 金兹堡模型\((U,f)\)的类似结论。我们表明扭曲德拉姆上同调\(\mathrm{H}^k_{\mathrm{dR}}(U,f)\)的非正则霍奇数在crepant双有理等价下是不变的。
英文摘要：
The Batyrev--Kontsevich theorem asserts that birational Calabi--Yau varieties have the same Hodge numbers. In this article, we prove an analogue for Landau--Ginzburg models $(U,f)$, where $U$ is a smooth quasi-projective complex variety and $f$ is a regular function on $U$. Under a natural non-degeneracy assumption, we show that the classes of such models in the localized Grothendieck ring of complex algebraic varieties with exponentials are invariant under crepant birational equivalences. Consequently, the irregular Hodge numbers of the twisted de Rham cohomology $\mathrm{H}^k_{\mathrm{dR}}(U,f)$ are invariant as well.
