Fibrations of low genus, I

被引：31

作者：

Catanese, Fabrizio

Pignatelli, Roberto

机构：

[1] Univ Bayreuth, Lehrstuhl Math 8, D-95447 Bayreuth, Germany

[2] Univ Trent, Dipartimento Matemat, I-38050 Povo, TN, Italy

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2006年 / 39卷 / 06期

关键词：

D O I：

10.1016/j.ansens.2006.10.001

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper we consider fibrations f : S -> B of an algebraic surface over a curve B, with general fibre a curve of genus g. Our main results are: (1) A structure theorem for such fibrations in the case where g = 2. (2) A structure theorem for such fibrations in the case where g = 3, the general fibre is nonhyperelliptic, and each fibre is 2-connected. (3) A theorem giving a complete description of the moduli space of minimal surfaces of general type with p(g) = q = 1, K-S(2) = 3, showing in particular that it has four unirational connected components. (4) Other applications of the two structure theorems. (c) 2006 Elsevier Masson SAS.

引用

页码：1011 / 1049

页数：39

共 43 条

[21]

Enriques F., 1949, Le Superficie Algebriche

[22]

ESNAULT H, 1990, COMPOS MATH, V76, P69

[23]

FRANCHETTA A, 1949, ATTI ACCAD NAZ SFMN, V6, P685

[24]

FRANCHETTA A, 1949, U ROMA I NAZ ALTA MA, V8, P423