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arXiv · 2209.02925

Index of coregularity zero log Calabi-Yau pairs

Stefano Filipazzi·Mirko Mauri·Joaquín Moraga
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Abstract

In this article, we study the index of log Calabi--Yau pairs $(X,B)$ of coregularity 0. We show that $2\lambda(K_X+B)\sim 0$, where $\lambda$ 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.

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Stefano Filipazzi, Mirko Mauri, Joaquín Moraga. 2022-09-07. Index of coregularity zero log Calabi-Yau pairs. https://doi.org/10.2140/ant.2025.19.383

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