论文标题
具有理性曲线周期的非Kählerian表面
Non Kählerian surfaces with a cycle of rational curves
论文作者
论文摘要
令$ s $为vii $ _0^+$的紧凑型复杂表面，其中包含一个有理曲线的周期$ c = \ sum d_j $。令$ d = c+a $是包含$ c $的最大连接的除数。如果曲线的另一个连接组件$ c'$，那么$ c'$是一个理性曲线的周期，$ a = 0 $，$ s $是inoue-hirzebruch表面。如果只有一个连接的组件$ d $，那么每个连接的组件$ a_i $ a $ a $是一条有理曲线，它与周期的曲线$ c_j $相交，并且对于每个链中的每一个曲线$ c_j $，在大多数链条上都符合$ c_j $。换句话说，我们不能证明存在曲线的存在循环$ c $的其他曲线，但是如果存在其他曲线，则最大除数看起来像是Kato表面的最大除数，也许曲线丢失。这种拓扑结果的证明是唐纳森定理在交叉形式和变形理论的琐碎化中的应用。我们将此结果应用于表明，扭曲的对数$ 1 $ - 形象具有微不足道的消失除数。
Let $S$ be a compact complex surface in class VII$_0^+$ containing a cycle of rational curves $C=\sum D_j$. Let $D=C+A$ be the maximal connected divisor containing $C$. If there is another connected component of curves $C'$ then $C'$ is a cycle of rational curves, $A=0$ and $S$ is a Inoue-Hirzebruch surface. If there is only one connected component $D$ then each connected component $A_i$ of $A$ is a chain of rational curves which intersects a curve $C_j$ of the cycle and for each curve $C_j$ of the cycle there at most one chain which meets $C_j$. In other words, we do not prove the existence of curves other those of the cycle $C$, but if some other curves exist the maximal divisor looks like the maximal divisor of a Kato surface with perhaps missing curves. The proof of this topological result is an application of Donaldson theorem on trivialization of the intersection form and of deformation theory. We apply this result to show that a twisted logarithmic $1$-form has a trivial vanishing divisor.
