Systoles, Special Lagrangians, and Bridgeland stability conditions

Yu-Wei Fan

Published 2018-03-26, updated 2018-11-12Version 2

We propose a natural generalization of Loewner's torus systolic inequality from the viewpoint of Calabi-Yau geometry. We ask whether the square of the minimum volume of special Lagrangians in a Calabi-Yau manifold is bounded by the total volume of the Calabi-Yau. We observe that this is related to a question of Bridgeland stability conditions on the derived category of Calabi-Yau manifolds, and we give an affirmative answer for generic K3 surfaces.