Systolic inequalities for K3 surfaces via stability conditions

Abstract

We introduce the notions of categorical systoles and categorical volumes of Bridgeland stability conditions on triangulated categories. We prove that for any projective K3 surface, there exists a constant C depending only on the rank and discriminant of its Picard group, such that $$\mathrm{sys}(\sigma {)}^2\le C\cdot \mathrm{vol}(\sigma )$$ holds for any stability condition on the derived category of coherent sheaves on the K3 surface. This is an algebro-geometric generalization of a classical systolic inequality on two-tori. We also discuss applications of this inequality in symplectic geometry.

26 pages; sync with the published version

References in corpus (7)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Calabi-Yau algebras
• Flat surfaces and stability structures
• Spaces of stability conditions
• Branes, Bundles and Attractors: Bogomolov and Beyond
• Weil-Petersson geometry on the space of Bridgeland stability conditions
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Cited by in corpus (1)

• An extension of the Siegel space of complex abelian varieties and conjectures on stability structures