{
  "id": "2408.17203",
  "version": "v1",
  "published": "2024-08-30T11:02:35.000Z",
  "updated": "2024-08-30T11:02:35.000Z",
  "title": "On L-equivalence for K3 surfaces and hyperkähler manifolds",
  "authors": [
    "Reinder Meinsma"
  ],
  "comment": "14 pages, comments are welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "This paper explores the relationship between L-equivalence and D-equivalence for K3 surfaces and hyperk\\\"ahler 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 hyperk\\\"ahler fourfolds and moduli spaces of sheaves on K3 surfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-30T11:02:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperkähler manifolds",
      "l-equivalence",
      "general l-equivalent k3 surfaces",
      "distinct lattice structures",
      "hodge theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}