Configurations of singular fibres on rational elliptic surfaces in characteristic two
Configurations of singular fibres on rational elliptic surfaces in characteristic two
复制标题
特征二有理椭圆面上奇异纤维的构型
DOI：
10.1080/00927870008827190
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发表时间：
2000
影响因子：
0.7
通讯作者：
W. Lang
中科院分区：
文献类型：
--
作者：
W. Lang
在[PI]中，U·Persson对复数上有理椭圆曲面上奇异纤维的所有可能构型进行了分类。他发现了279种不同的配置。R·米兰达在[MI]中用一种更具组合性的方法重新列出了Persson的清单。在本文中，我们在第二个特征中进行了这种分类。我们发现有147种不同的配置是可能的。特征二的问题比特征零的问题简单。我们将在下面简要讨论这方面的原因。我们研究调和二的代数闭域k。设f：X-+P_1是k上的有理椭圆曲面，我们假设(就像Persson和Miranda一样)我们的曲面是相对极小的(纤维中没有例外曲线)，并且f有一个截面。然后我们的曲面有魏尔斯特拉斯方程y2+a L xy+a3y=x3+a2x2+aq x+a6，
In [PI, U. Persson classified all possible configurations of singular fibres on rational elliptic surfaces over the complex numbers. He found 279 different configurations. Persson's list was redone by R. Miranda in [MI, using a more combinatorial method. In the present paper, we carry out this classification in characteristic two. We find that 147 different configurations are possible. The problem is simpler in characteristic two than in characteristic zero. We will discuss the reasons for this briefly below. We work over an algebraically closed field k of ~haract~eristic two. Let f : X --+ P1 be a rational elliptic surface over k. We will assume (as did Persson and Miranda) that our surface is relatively minimal (no ex~ept~ional curves in the fibres) and that f has a section. Then our surface has Weierstrass equation Y2 + a l x y + a3y = x3 + a2x2 + a q x + a6,