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Mathematics > Algebraic Geometry

arXiv:1812.02735 (math)
[Submitted on 5 Dec 2018 (v1), last revised 9 Jul 2019 (this version, v3)]

Title:Discriminants of stable rank two sheaves on some general type surfaces

Authors: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.
Comments: 16 pages, Third Version: Minor Changes
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14J60 (Primary), 14D20, 14F05 (Secondary)
Cite as: arXiv:1812.02735 [math.AG]
  (or arXiv:1812.02735v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.02735

Submission history

From: Benjamin Schmidt [view email]
[v1] Wed, 5 Dec 2018 21:36:58 UTC (21 KB)
[v2] Thu, 10 Jan 2019 21:55:36 UTC (21 KB)
[v3] Tue, 9 Jul 2019 07:21:29 UTC (22 KB)
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