Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917660193718272 |
|---|---|
| author | Markman, Eyal |
| author_facet | Markman, Eyal |
| contents | Let X and Y be compact hyper-Kahler manifolds deformation equivalence to the Hilbert scheme of length n subschemes of a K3 surface. A cohomology class in their product XxY is an analytic correspondence, if it belongs to the subring generated by Chern classes of coherent analytic sheaves. Let f be a Hodge isometry of their second rational cohomologies with respect to the Beauville-Bogomolov-Fujiki pairings. We prove that f is induced by an analytic correspondence. We furthermore lift f to an analytic correspondence F between their total rational cohomologies, which is a Hodge isometry with respect to the Mukai pairings, and which preserves the gradings up to sign. When X and Y are projective the correspondences f and F are algebraic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_00516 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic Markman, Eyal Algebraic Geometry Let X and Y be compact hyper-Kahler manifolds deformation equivalence to the Hilbert scheme of length n subschemes of a K3 surface. A cohomology class in their product XxY is an analytic correspondence, if it belongs to the subring generated by Chern classes of coherent analytic sheaves. Let f be a Hodge isometry of their second rational cohomologies with respect to the Beauville-Bogomolov-Fujiki pairings. We prove that f is induced by an analytic correspondence. We furthermore lift f to an analytic correspondence F between their total rational cohomologies, which is a Hodge isometry with respect to the Mukai pairings, and which preserves the gradings up to sign. When X and Y are projective the correspondences f and F are algebraic. |
| title | Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2204.00516 |