Duke Mathematical Journal

The Bogomolov–Miyaoka–Yau inequality for logarithmic surfaces in positive characteristic

Adrian Langer

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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.

Article information

Duke Math. J., Volume 165, Number 14 (2016), 2737-2769.

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

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Zentralblatt MATH identifier

Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Secondary: 14G17: Positive characteristic ground fields 14J29: Surfaces of general type

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


Langer, Adrian. The Bogomolov–Miyaoka–Yau inequality for logarithmic surfaces in positive characteristic. Duke Math. J. 165 (2016), no. 14, 2737--2769. doi:10.1215/00127094-3627203. https://projecteuclid.org/euclid.dmj/1464872424

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