On Chern classes of Lagrangian fibered hyper-Kähler manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916168826093568 |
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| author | Voisin, Claire |
| author_facet | Voisin, Claire |
| contents | We study the rank stratification for the differential of a Lagrangian fibration over a smooth basis. We also introduce and study the notion of Lagrangian morphism of vector bundles. As a consequence, we prove some of the vanishing, in the Chow groups of a Lagrangian fibered hyper-Kähler variety $X$, of certain polynomials in the Chern classes of $X$ and the Lagrangian divisor, predicted by the Beauville-Voisin conjecture. Under some natural assumptions on the dimensions of the rank strata, we also establish nonnegativity and positivity results for Chern classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09396 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Chern classes of Lagrangian fibered hyper-Kähler manifolds Voisin, Claire Algebraic Geometry We study the rank stratification for the differential of a Lagrangian fibration over a smooth basis. We also introduce and study the notion of Lagrangian morphism of vector bundles. As a consequence, we prove some of the vanishing, in the Chow groups of a Lagrangian fibered hyper-Kähler variety $X$, of certain polynomials in the Chern classes of $X$ and the Lagrangian divisor, predicted by the Beauville-Voisin conjecture. Under some natural assumptions on the dimensions of the rank strata, we also establish nonnegativity and positivity results for Chern classes. |
| title | On Chern classes of Lagrangian fibered hyper-Kähler manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2305.09396 |