Covers of elliptic curves and the moduli space of stable curves

被引：11

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

共 34 条

[1]

[Anonymous], ARXIVMATH0205056

[2]

Arbarello E., 1985, Geometry of Algebraic Curves

[3] Euler characteristics of Teichmuller curves in genus two [J].

Bainbridge, Matt .

GEOMETRY & TOPOLOGY, 2007, 11 :1887-2073

[4] A page on Eisenstein series in Ramanujan's lost notebook [J].

Berndt, BC ;

Yee, AJ .

GLASGOW MATHEMATICAL JOURNAL, 2003, 45 :123-129

[5]

CHANG MC, 1991, J DIFFER GEOM, V34, P267

[6] SOME DENSITY RESULTS FOR CURVES WITH NONSIMPLE JACOBIANS [J].

COLOMBO, E ;

PIROLA, GP .

MATHEMATISCHE ANNALEN, 1990, 288 (01) :161-178

[7]

CORNALBA M, 1988, ANN SCI ECOLE NORM S, V21, P455

[8] The Effective Cone of the Kontsevich Moduli Space [J].

Coskun, Izzet ;

Harris, Joe ;

Starr, Jason .

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2008, 51 (04) :519-534

[9] THE KODAIRA DIMENSION OF THE MODULI SPACE OF CURVES OF GENUS-GREATER-THAN-OR-EQUAL-TO-23 [J].

EISENBUD, D ;

HARRIS, J .

INVENTIONES MATHEMATICAE, 1987, 90 (02) :359-387

[10] Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials [J].

Eskin, A ;

Okounkov, A .

INVENTIONES MATHEMATICAE, 2001, 145 (01) :59-103

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