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arXiv · 1412.0256

On algebraic surfaces of general type with negative c2

Yi Gu
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Abstract

We prove that for any prime number $p\ge 3$, there exists a positive number $\kappa_p$ such that $\chi(\mathcal{O}_X)\ge \kappa_pc_1^2$ holds true for all algebraic surfaces $X$ of general type in characteristic $p$. In particular, $\chi(\mathcal{O}_X)>0$. This answers a question of N. Shepherd-Barron when $p\ge 3$.

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Yi Gu. 2014-11-30. On algebraic surfaces of general type with negative c2. https://doi.org/10.1112/s0010437x16007491

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