False Hyperelliptic Surfaces with Section
False Hyperelliptic Surfaces with Section
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带截面的假超椭圆曲面
DOI：
10.1002/mana.19941670113
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发表时间：
2006
影响因子：
1
通讯作者：
Yoshifumi Takeda Nara
中科院分区：
文献类型：
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作者：
Yoshifumi Takeda Nara
设X是特征p > 0的代数闭域上的非奇异相对极小射影曲面。我们称X为伪超椭圆曲面，如果X满足下列条件：（1）c2（X）= 0，c1（X）2 = 0，dim Alb（X）= 1，（2）X的Albanese映射的所有纤维都是有理曲线，只有一个xpv + yn = 0型尖点。本文考虑了一类伪超椭圆曲面，其Albanese映射具有横截面。证明了每一个有截面的伪超椭圆曲面都是由一个椭圆直纹曲面产生的，并且每一个伪超椭圆曲面都有一个带多重纤维的椭圆纤维化。此外，我们还构造了一个伪超椭圆曲面的例子，它的椭圆纤维化具有pv（v > 1）重超奇异椭圆曲线的重纤维。
Let X be a nonsingular relatively minimal projective surface over an algebraically closed field of characteristic p > 0. We call X a false hyperelliptic surface if X satisfies the following conditions: (1) c2(X) = 0, c1(X)2 = 0, dim Alb (X) = 1, and (2) All fibres of the Albanese mapping of X are rational curves with only one cusp of type xpv + yn = 0. In this article, we consider a false hyperelliptic surface whose Albanese mapping has a cross-section. We prove that every false hyperellyptic surface with section arises from an elliptic ruled surface and that every false hyperelliptic surface has an elliptic fibration with multiple fibre. Moreover, we construct an example of false hyperelliptic surface with section, whose elliptic fibration has a multiple fibre of supersingular elliptic curve of multiplicity pv (v > 1).