Abstract
Abstract We prove a version of the Bogomolov–Gieseker (BG) inequality on smooth projective surfaces of general type in positive characteristic. Our result is stronger than a similar theorem by Langer for vector bundles of sufficiently large rank. Our inequality enables us to construct Bridgeland stability conditions with the full support property on all smooth projective surfaces in positive characteristic. We also prove the BG-type inequality for higher dimensional varieties.
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