论文标题
$ C_1^2 = 9 $和$χ= 5 $的表面，其规范类别可除以$ 3 $
Surfaces with $c_1^2 =9$ and $χ=5$ whose canonical classes are divisible by $3$
论文作者
论文摘要
我们将使用$ c^2 = 9 $和$χ= 5 $研究最小的复杂表面，其规范类别在整体共同体学组中可除以$ 3 $，其中$ c_1^2 $和$χ$分别表示代数表面的第一个Chern数量，分别是结构的欧拉（Euler）特征。主要的结果是此类表面的结构定理，模量空间的不合理性以及规范图的行为的描述。作为副产品，我们还将排除ciliberto--francia--francia--Mendes Lopes中提到的某个案例。由于不规则性$ q $在我们的表面消失，因此我们的表面具有几何属$ p_g = 4 $。
We shall study minimal complex surfaces with $c^2 = 9$ and $χ=5$ whose canonical classes are divisible by $3$ in the integral cohomology groups, where $c_1^2$ and $χ$ denote the first Chern number of an algebraic surface and the Euler characteristic of the structure sheaf, respectively. The main results are a structure theorem for such surfaces, the unirationality of the moduli space, and a description of the behavior of the canonical map. As a byproduct, we shall also rule out a certain case mentioned in a paper by Ciliberto--Francia--Mendes Lopes. Since the irregularity $q$ vanishes for our surfaces, our surfaces have geometric genus $p_g = 4$.
