Derived Partners of Enriques Surfaces
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916662371942400 |
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| author | Borisov, Lev Chan, Vernon Wang, Chengxi |
| author_facet | Borisov, Lev Chan, Vernon Wang, Chengxi |
| contents | Let $V$ be a $6$-dimensional complex vector space with an involution $σ$ of trace $0$, and let $W \subset \Sym^2 V^\vee$ be a generic $3$-dimensional subspace of $σ$-invariant quadratic forms. To these data we can associate an Enriques surface as the $σ$-quotient of the complete intersection of the quadratic forms in $W$. We exhibit noncommutative Deligne-Mumford stacks together with sheaves of Azumaya algebras on them whose derived categories are equivalent to those of the Enriques surfaces. This provides a more accessible treatment of of Theorem 6.16 in https://www.ams.org/journals/jams/2021-34-02/S0894-0347-2021-00963-3/ .. We also construct geometric realizations of the Brauer classes coming from these sheaves of Azumaya algebras which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_07768 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Derived Partners of Enriques Surfaces Borisov, Lev Chan, Vernon Wang, Chengxi Algebraic Geometry Let $V$ be a $6$-dimensional complex vector space with an involution $σ$ of trace $0$, and let $W \subset \Sym^2 V^\vee$ be a generic $3$-dimensional subspace of $σ$-invariant quadratic forms. To these data we can associate an Enriques surface as the $σ$-quotient of the complete intersection of the quadratic forms in $W$. We exhibit noncommutative Deligne-Mumford stacks together with sheaves of Azumaya algebras on them whose derived categories are equivalent to those of the Enriques surfaces. This provides a more accessible treatment of of Theorem 6.16 in https://www.ams.org/journals/jams/2021-34-02/S0894-0347-2021-00963-3/ .. We also construct geometric realizations of the Brauer classes coming from these sheaves of Azumaya algebras which may be of independent interest. |
| title | Derived Partners of Enriques Surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2108.07768 |