On the Bogomolov-Gieseker inequality for tame Deligne-Mumford surfaces
We generalize the Bogomolov-Gieseker inequality for semistable coherent sheaves on smooth projective surfaces to smooth Deligne-Mumford surfaces. We work over positive characteristic \(p>0\) and generalize Langer's method to smooth Deligne-Mumford stacks. As applications we obtain the Bogomo...
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Veröffentlicht in: | arXiv.org 2021-04 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | We generalize the Bogomolov-Gieseker inequality for semistable coherent sheaves on smooth projective surfaces to smooth Deligne-Mumford surfaces. We work over positive characteristic \(p>0\) and generalize Langer's method to smooth Deligne-Mumford stacks. As applications we obtain the Bogomolov inequality for semistable coherent sheaves on a Deligne-Mumford surface in characteristic zero, and the Bogomolov inequality for semistable sheaves on a root stack over a smooth surface which is equivalent to the Bogomolov inequality for the rational parabolic sheaves on a smooth surface \(S\). In a joint appendix with Hao Max Sun, we generalize the Bogomolov inequality formula to Simpson Higgs sheaves on tame Deligne-Mumford stacks. |
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ISSN: | 2331-8422 |