On classification of isotrivial elliptic Belyi fibrations
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摘要: 本文对$\mathbb{P}^1$上带有三条奇异纤维的常模椭圆纤维化(简称Belyi纤维化)进行了分类， 给出了精确的12类带有截面的Belyi纤维化.作为这一分类的推论，还发现，除了一种情形外，其余情形对应的$\overline{\mathcal{M}}_1$中的轨迹都是零维的.Abstract: In this paper we classify relatively minimal, isotrivial families of curves $f: S \to \mathbb{P}^1$ of genus 1 with three singular fibers (Belyi fibrations). Assuming that these families have a section, we find that they are exactly 12 in number up to isomorphism. Moreover, as a result of this classification, we find that except one, the dimension of all other families in $\overline{\mathcal{M}}_1$ is zero.
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[1] [1] BARTH W, HULEK K, PETERS C, et al. Compact Complex Surfaces [M]. Berlin: Springer, 2004.
[2] BELYI G V. On Galois extensions of a maximal cyclotomic field [J]. Math USSR Izv, 1980, 14(2): 247-256.
[3] GONG C, LU J, TAN S L. On the classification and Mordell-Weil groups of families of curves with two singular fibers [J]. preprint.
[4] SCHMICKLER-HIRZEBRUCH U. Elliptische fl¨achen ¨uber P1C mit drei Ausnahmefasern und die hypergeometrische Differentialgleichung [M]. M¨unster: Universit¨at M¨unster, 1985.
[5] LU J, TAN S L. Inequalities between the Chern numbers of a singular fiber in a family of algebraic curves [J]. Trans Amer Math Soc, 2013, 365: 3373-3396.
[ 6 ] MIRANDA R. The Basic Theory of Elliptic Surfaces [R]. Fort Collins, Colorado: Colorado State Univ, 1989.
[ 7 ] TAN S L. On the base changes of pencils of curves, I [J]. Manusc Math, 1994, 84: 225-244.
[ 8 ] TAN S L. On the base changes of pencils of curves, II [J]. Math Z, 1996, 222: 655-676.
[ 9 ] TAN S L. Chern numbers of a singular fiber, modular invariants and isotrivial families of curves [J]. Acta Math Vietnam, 2010, 35: 159-172. -
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