Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber
Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber
复制标题
具有独特奇异纤维的纤维属三的 Catanese-Ciliberto 表面
DOI：
10.2748/tmj/1145390205
复制
发表时间：
2006
影响因子：
0.5
通讯作者：
H. Ishida
中科院分区：
文献类型：
--
作者：
H. Ishida
.本文研究了一般类型的极小曲面，其中pg = q = 1，K2 S = 3，我们称之为Catanese-Ciliberto曲面.该曲面的Albanese映射给出了椭圆曲线上的曲线纤维化。对于任意椭圆曲线E，我们得到了满足Alb（S）≠ E的Catanese-Ciliberto曲面，该曲面没有（− 2）-曲线，且有唯一的奇异纤维。此外，我们证明了满足这些条件的同构类的数量是四个，如果E没有复乘型自同构。
. In this paper, we study a minimal surface of general type with p g = q = 1 , K 2 S = 3 which we call a Catanese-Ciliberto surface. The Albanese map of this surface gives a fibration of curves over an elliptic curve. For an arbitrary elliptic curve E , we obtain the Catanese-Ciliberto surface which satisfies Alb (S) ∼= E , has no ( − 2 ) -curves and has a unique singular fiber. Furthermore, we show that the number of the isomorphism classes satisfying these conditions is four if E has no automorphism of complex multiplication type.