Covers of elliptic curves and the moduli space of stable curves

被引：10

作者：

Chen, Dawei ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2010年 / 649卷

关键词：

KODAIRA DIMENSION; TEICHMULLER-CURVES; EFFECTIVE DIVISORS; EFFECTIVE CONE; SURFACES; GENUS-2; SLOPES;

D O I：

10.1515/CRELLE.2010.092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider genus g curves that admit degree d covers of an elliptic curve. Varying a branch point, we get a one-parameter family W of simply branched covers. Varying the target elliptic curve, we get another one-parameter family Y of covers that have a unique branch point. We investigate the geometry of W and Y by using admissible covers to study their slopes, genera and components. The results can be applied to study slopes of effective divisors on the moduli space of stable genus g curves.

引用

页码：167 / 205

页数：39

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