论文标题
在光滑的投影表面上的边界共同体，皮卡德编号2
Bounding cohomology on a smooth projective surface with Picard number 2
论文作者
论文摘要
以下猜想是由于B. Harbourne，J.Roé，C。Cilberto和R. Miranda之间的讨论引起的：对于光滑的投射表面$ x $，存在正常的$ C_X $，因此$ h^1（\ Mathcal o_x（c）（c））当Picard Number $ρ（x）= 2 $时，我们证明，如果Kodaira dimension $κ（x）= 1 $，而$ x $具有负曲线或$ x $具有两个负曲线，那么此猜想将以$ x $的速度保留。
The following conjecture arose out of discussions between B. Harbourne, J. Roé, C. Cilberto and R. Miranda: for a smooth projective surface $X$ there exists a positive constant $c_X$ such that $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ for every prime divisor $C$ on $X$. When the Picard number $ρ(X)=2$, we prove that if either the Kodaira dimension $κ(X)=1$ and $X$ has a negative curve or $X$ has two negative curves, then this conjecture holds for $X$.
