Publikationsdatum:
2016-05-29
Beschreibung:
We show that for many moduli spaces $ {\mathcal M}$ of torsion sheaves on K3 surfaces $S$ , the functor $D^b(S) \to D^b( {\mathcal M})$ induced by the universal sheaf is a $ {\mathbb P}$ -functor, hence can be used to construct an autoequivalence of $D^b( {\mathcal M})$ , and that this autoequivalence can be factored into geometrically meaningful equivalences associated to abelian fibrations and Mukai flops. Along the way, we produce a derived equivalence between two compact hyperkähler $2g$ -folds that are not birational, for every $g \ge 2$ . We also speculate about an approach to showing that birational moduli spaces of sheaves on K3 surfaces are derived equivalent.
Print ISSN:
0024-6107
Digitale ISSN:
1469-7750
Thema:
Mathematik
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