On algebraic surfaces of general type with negative $c_{2}$
On algebraic surfaces of general type with negative $c_{2}$
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在具有负 $c_{2}$ 的一般类型代数曲面上
DOI：
10.1112/s0010437x16007491
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发表时间：
2014
影响因子：
1.8
通讯作者：
Yi Gu
中科院分区：
文献类型：
--
作者：
Yi Gu
We prove that for any prime number $p\geqslant 3$ , there exists a positive number $\unicode[STIX]{x1D705}_{p}$ such that $\unicode[STIX]{x1D712}({\mathcal{O}}_{X})\geqslant \unicode[STIX]{x1D705}_{p}c_{1}^{2}$ holds true for all algebraic surfaces $X$ of general type in characteristic $p$ . In particular, $\unicode[STIX]{x1D712}({\mathcal{O}}_{X})>0$ . This answers a question of Shepherd-Barron when $p\geqslant 3$ .
We prove that for any prime number $p\geqslant 3$ , there exists a positive number $\unicode[STIX]{x1D705}_{p}$ such that $\unicode[STIX]{x1D712}({\mathcal{O}}_{X})\geqslant \unicode[STIX]{x1D705}_{p}c_{1}^{2}$ holds true for all algebraic surfaces $X$ of general type in characteristic $p$ . In particular, $\unicode[STIX]{x1D712}({\mathcal{O}}_{X})>0$ . This answers a question of Shepherd-Barron when $p\geqslant 3$ .