A two-dimensional family of surfaces of general type with p(g)=0 and K-2=7
A two-dimensional family of surfaces of general type with p(g)=0 and K-2=7
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p(g)=0 且 K-2=7 的一般类型二维曲面族
DOI：
10.1016/j.aim.2020.107551
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发表时间：
2021
影响因子：
1.7
通讯作者：
Shin YongJoo
中科院分区：
文献类型：
--
作者：
Chen Yifan;Shin YongJoo
研究了pg(S)=0，K S 2=7的复极小光滑曲面S的构造。井上构造了这类曲面的第一个例子，可以描述为四节点三次曲面上的Galois Z/2Z×Z/2Z-覆盖。后来，第一个命名的作者构造了更多的例子，如Galois Z/2 Z×Z/2 Z-覆盖在某些一次六节点del Pezzo曲面上。本文构造了一个二维Pg=0，K2=7的二维极小光滑曲面族，作为Picard数为3，有8个结点，有两个椭圆曲线的有理曲面的Galois Z/2 Z×Z/2 Z-覆盖.这个家庭不同于以前的家庭。
We study the construction of complex minimal smooth surfaces S of general type with p g (S)= 0 and K S 2= 7. Inoue constructed the first examples of such surfaces, which can be described as Galois Z/2 Z× Z/2 Z-covers over the four-nodal cubic surface. Later the first named author constructed more examples as Galois Z/2 Z× Z/2 Z-covers over certain six-nodal del Pezzo surfaces of degree one. In this paper we construct a two-dimensional family of minimal smooth surfaces of general type with p g= 0 and K 2= 7, as Galois Z/2 Z× Z/2 Z-covers of certain rational surfaces with Picard number three, with eight nodes and with two elliptic fibrations. This family is different from the previous ones.