Discriminants of stable rank two sheaves on some general type surfaces

Benjamin Schmidt; Benjamin Sung

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arXiv · 1812.02735

Discriminants of stable rank two sheaves on some general type surfaces

Benjamin Schmidt·Benjamin Sung

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Abstract

We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We then proceed to describe the surface itself as a moduli space of rank two vector bundles on it. Lastly, we give a proof of the Bogomolov inequality for semistable rank two sheaves on integral surfaces in three-dimensional projective space in all characteristics.

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Benjamin Schmidt, Benjamin Sung. 2018-12-05. Discriminants of stable rank two sheaves on some general type surfaces. https://arxiv.org/abs/1812.02735

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