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Title:
Systolic inequality for K3 surfaces via stability conditions
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Abstract:
The connection between flat surfaces and stability conditions has been established by Gaiotto-Moore-Neitzke, Bridgeland-Smith and Haiden-Katzarkov-Kontsevich. Motivated by this connection, we define a categorical analogue of 'systole' in terms of stability conditions. We prove that the systoles of stability conditions on certain K3 surfaces are bounded above by the square roots of the volumes of K3 surfaces. This is a generalization of Loewner’s torus systolic inequality from the perspective of Calabi-Yau geometry.
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