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1 October 2016 The Bogomolov–Miyaoka–Yau inequality for logarithmic surfaces in positive characteristic
Adrian Langer
Duke Math. J. 165(14): 2737-2769 (1 October 2016). DOI: 10.1215/00127094-3627203

Abstract

We generalize Bogomolov’s inequality for Higgs sheaves and the Bogomolov– Miyaoka–Yau inequality in positive characteristic to the logarithmic case. We also generalize Shepherd-Barron’s results on Bogomolov’s inequality on surfaces of special type from rank 2 to the higher-rank case. We use these results to show some examples of smooth nonconnected curves on smooth rational surfaces that cannot be lifted modulo p2. These examples contradict some claims by Xie.

Citation

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Adrian Langer. "The Bogomolov–Miyaoka–Yau inequality for logarithmic surfaces in positive characteristic." Duke Math. J. 165 (14) 2737 - 2769, 1 October 2016. https://doi.org/10.1215/00127094-3627203

Information

Received: 29 August 2014; Revised: 12 October 2015; Published: 1 October 2016
First available in Project Euclid: 2 June 2016

zbMATH: 06653511
MathSciNet: MR3551772
Digital Object Identifier: 10.1215/00127094-3627203

Subjects:
Primary: 14J60
Secondary: 14G17 , 14J29

Keywords: Bogomolov’s inequality , Bogomolov-Miyaoka-Yau inequality , logarithmic Higgs sheaves , positive characteristic

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 14 • 1 October 2016
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