The geometry of antisymplectic involutions, II
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914508111347712 |
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| author | Flapan, Laure Macrì, Emanuele O'Grady, Kieran G. Saccà, Giulia |
| author_facet | Flapan, Laure Macrì, Emanuele O'Grady, Kieran G. Saccà, Giulia |
| contents | We continue our study of fixed loci of antisymplectic involutions on projective hyper-Kähler manifolds of $\mathrm{K3}^{[n]}$-type induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice. We prove that if the divisibility of the ample class is 2, then one connected component of the fixed locus is a Fano manifold of index 3, thus generalizing to higher dimensions the case of the LLSvS 8-fold associated to a cubic fourfold. We also show that, in the case of the LLSvS 8-fold associated to a cubic fourfold, the second component of the fixed locus is of general type, thus answering a question by Manfred Lehn. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02238 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The geometry of antisymplectic involutions, II Flapan, Laure Macrì, Emanuele O'Grady, Kieran G. Saccà, Giulia Algebraic Geometry 14C20, 14D06, 14D20, 14F08, 14J42, 14J45, 14J60 We continue our study of fixed loci of antisymplectic involutions on projective hyper-Kähler manifolds of $\mathrm{K3}^{[n]}$-type induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice. We prove that if the divisibility of the ample class is 2, then one connected component of the fixed locus is a Fano manifold of index 3, thus generalizing to higher dimensions the case of the LLSvS 8-fold associated to a cubic fourfold. We also show that, in the case of the LLSvS 8-fold associated to a cubic fourfold, the second component of the fixed locus is of general type, thus answering a question by Manfred Lehn. |
| title | The geometry of antisymplectic involutions, II |
| topic | Algebraic Geometry 14C20, 14D06, 14D20, 14F08, 14J42, 14J45, 14J60 |
| url | https://arxiv.org/abs/2309.02238 |