On L-equivalence for K3 surfaces and hyperkähler manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908860606840832 |
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| author | Meinsma, Reinder |
| author_facet | Meinsma, Reinder |
| contents | This paper explores the relationship between L-equivalence and D-equivalence for K3 surfaces and hyperkähler manifolds. Building on Efimov's approach using Hodge theory, we prove that very general L-equivalent K3 surfaces are D-equivalent, leveraging the Derived Torelli Theorem for K3 surfaces. Our main technical contribution is that two distinct lattice structures on an integral, irreducible Hodge structure are related by a rational endomorphism of the Hodge structure. We partially extend our results to hyperkähler fourfolds and moduli spaces of sheaves on K3 surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17203 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On L-equivalence for K3 surfaces and hyperkähler manifolds Meinsma, Reinder Algebraic Geometry This paper explores the relationship between L-equivalence and D-equivalence for K3 surfaces and hyperkähler manifolds. Building on Efimov's approach using Hodge theory, we prove that very general L-equivalent K3 surfaces are D-equivalent, leveraging the Derived Torelli Theorem for K3 surfaces. Our main technical contribution is that two distinct lattice structures on an integral, irreducible Hodge structure are related by a rational endomorphism of the Hodge structure. We partially extend our results to hyperkähler fourfolds and moduli spaces of sheaves on K3 surfaces. |
| title | On L-equivalence for K3 surfaces and hyperkähler manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.17203 |