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<p>This paper explores the relationship between <i>L</i>-equivalence and <i>D</i>-equivalence for K3 surfaces and hyperkähler manifolds. Building on Efimov’s approach using Hodge theory, we prove that very general <i>L</i>-equivalent K3 surfaces are <i>D</i>-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.</p>

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On L-equivalence for K3 Surfaces and Hyperkähler Manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月26日

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  • Reinder Meinsma

摘要

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.