论文标题
在表面上的BMY不平等
On the BMY inequality on surfaces
论文作者
论文摘要
在本文中，我们关注一般类型表面的顺序与BMY不平等的失败之间的关系。我们认为可半固定的纤维$π：s \ longrightArrow c $，其中$ s $是光滑的投影表面，$ c $是一条光滑的投影曲线。使用$ S $，$ c $和$ s/c $上本地确切的差分表格的确切序列，我们证明了与普通表面相关的不平等，与$ C_1^2 $和$ C_2 $相关，该表面承认通常是普通的可半固定纤维。这种不平等与BMY不等式的不同之处在于校正术语，如果纤维是普通的，则消失。
In this paper, we are concerned with the relation between the ordinarity of surfaces of general type and the failure of the BMY inequality in positive characteristic. We consider semistable fibrations $π:S \longrightarrow C$ where $S$ is a smooth projective surface and $C$ is a smooth projective curve. Using the exact sequence relating the locally exact differential forms on $S$, $C$, and $S/C$, we prove an inequality relating $c_1^2$ and $c_2$ for ordinary surfaces which admit generically ordinary semistable fibrations. This inequality differs from the BMY inequality by a correcting term which vanishes if the fibration is ordinary.
