Index of coregularity zero log Calabi-Yau pairs
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916595927875584 |
|---|---|
| author | Filipazzi, Stefano Mauri, Mirko Moraga, Joaquín |
| author_facet | Filipazzi, Stefano Mauri, Mirko Moraga, Joaquín |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02925 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Index of coregularity zero log Calabi-Yau pairs Filipazzi, Stefano Mauri, Mirko Moraga, Joaquín Algebraic Geometry 14B05, 14E30, 14L24, 14M25 (Primary), 14A20, 53D20 (Secondary) 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. |
| title | Index of coregularity zero log Calabi-Yau pairs |
| topic | Algebraic Geometry 14B05, 14E30, 14L24, 14M25 (Primary), 14A20, 53D20 (Secondary) |
| url | https://arxiv.org/abs/2209.02925 |