论文标题
核心索引零log calabi-yau对
Index of coregularity zero log Calabi-Yau pairs
论文作者
论文摘要
在本文中，我们研究了log calabi-yyau对$（x，b）$ coregularity 0的索引。我们证明$2λ（k_x+b）\ sim 0 $，其中$λ$是$（x，b）$的weil索引。这与klt calabi-yau品种形成鲜明对比的是，该索引可以与尺寸达到双重生长。我们在索引上的尖锐界限扩展到广义的log calabi-yau对，半gog典型对以及孤立的对数典型的核心性奇异性0。最后，我们讨论了对Calabi-Yau品种的应用，并具有有限的群体作用，包括纯纯种非糖自态的全身形态符合性品种。
In this article, we study the index of log Calabi--Yau pairs $(X,B)$ of coregularity 0. We show that $2λ(K_X+B)\sim 0$, where $λ$ is the Weil index of $(X,B)$. This is in contrast to the case of klt Calabi--Yau varieties, where the index can grow doubly exponentially with the dimension. Our sharp bound on the index extends to the context of generalized log Calabi--Yau pairs, semi-log canonical pairs, and isolated log canonical singularities of coregularity 0. As a consequence, we show that the index of a variety appearing in the Gross--Siebert program or in the Kontsevich--Soibelman program is at most $2$. Finally, we discuss applications to Calabi--Yau varieties endowed with a finite group action, including holomorphic symplectic varieties endowed with a purely non-symplectic automorphism.
