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arXiv · 1903.04158

Slope inequalities and a Miyaoka-Yau type inequality

Yi Gu·Xiaotao Sun·Mingshuo Zhou
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Abstract

For a minimal smooth projective surface $S$ of general type over a field of characteristic $p>0$, we prove that $K^2_S\le 32\chi(\cal{O}_S).$ Moreover, if $18\chi(\cal{O}_S) 0$, which answers completely a question of Shepherd-Barron.

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Yi Gu, Xiaotao Sun, Mingshuo Zhou. 2019-03-11. Slope inequalities and a Miyaoka-Yau type inequality. https://arxiv.org/abs/1903.04158

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