Constructions of derived equivalent hyper-K\"ahler fourfolds

Grzegorz Kapustka; Micha{\l} Kapustka

Constructions of derived equivalent hyper-K\"ahler fourfolds

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arxiv 2312.14543 v5 pith:WUV3HEXI submitted 2023-12-22 math.AG

Grzegorz Kapustka , Micha{l} Kapustka This is my paper · ORCID

classification math.AG

keywords ahlerderivedhyper-kequivalentfourfoldsconstructionspicardrank

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abstract

We study twisted derived equivalences of hyper-K\"ahler fourfolds. We describe when two hyper-K\"ahler fourfolds of $K3^{[2]}$-type of Picard rank $1$ with isomorphic transcendental lattices are derived equivalent. Then we present new constructions of pairs of twisted derived equivalent hyper-K\"ahler manifolds of Picard rank $\geq 2$.

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A twisted derived category of hyper-K\"ahler varieties of $K3^{[n]}$-type
math.AG 2025-02 accept novelty 6.0 of 10

A twisted derived category of K3^[n]-type hyper-Kähler varieties is governed by the oriented Markman-Mukai lattice, proven under a primitivity condition and yielding derived equivalences between fine K3 moduli spaces ...

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