Some density results for hyperkähler manifolds
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911392579190784 |
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| author | Dutta, Yajnaseni Izadi, Elham Kamenova, Ljudmila Marquand, Lisa |
| author_facet | Dutta, Yajnaseni Izadi, Elham Kamenova, Ljudmila Marquand, Lisa |
| contents | Lagrangian fibrations of hyperkähler manifolds are induced by semi-ample line bundles which are isotropic with respect to the Beauville-Bogomolov-Fujiki form. For a non-isotrivial family of hyperkähler manifolds over a complex manifold $S$ of positive dimension, we prove that the set of points in $S$, for which there is an isotropic class in the Picard lattice of the corresponding hyperkähler manifold represented as a fiber over that point, is analytically dense in $S$. We also prove the expected openness and density of the locus of polarised hyperkähler manifolds that admit a nef algebraic isotropic line bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04868 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some density results for hyperkähler manifolds Dutta, Yajnaseni Izadi, Elham Kamenova, Ljudmila Marquand, Lisa Algebraic Geometry 14D05, 14D06, 14J42, 37J38 Lagrangian fibrations of hyperkähler manifolds are induced by semi-ample line bundles which are isotropic with respect to the Beauville-Bogomolov-Fujiki form. For a non-isotrivial family of hyperkähler manifolds over a complex manifold $S$ of positive dimension, we prove that the set of points in $S$, for which there is an isotropic class in the Picard lattice of the corresponding hyperkähler manifold represented as a fiber over that point, is analytically dense in $S$. We also prove the expected openness and density of the locus of polarised hyperkähler manifolds that admit a nef algebraic isotropic line bundle. |
| title | Some density results for hyperkähler manifolds |
| topic | Algebraic Geometry 14D05, 14D06, 14J42, 37J38 |
| url | https://arxiv.org/abs/2403.04868 |