The Fundamental Group of the Complement of the Branch Curve of CP^1×T

作     者：Meirav AMRAM Michael FRIEDMAN Mina TEICHER 

作者机构：Department of Mathematics Bar-Ilan University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2009年第25卷第9期

页      面：1443-1458页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by DAAD EU-network HPRN-CT-2009-00099(EAGER) The Emmy Noether Research Institute for Mathematics the Minerva Foundation of Germany The Israel Science Foun dation grant #8008/02-3 (Excellency Center "Group Theoretic Methods in the Study of Algebraic Varieties") 

主　　题：fundamental group generic projection curves and singularities branch curve 

摘      要：Denoting by T the complex projective torus, we can embed the surface CP^1 × T in CP^5. In this paper we compute the fundamental group of the complement of the branch curve of this surface. Since the embedding is not ＂ample enough＂, the embedded surface does not belong to the classes of surfaces where the fundamental group is virtually solvable： a property which holds for these groups for ＂ample enough＂ embeddings. On the other hand, as it is the first example of this computation for non simply-connected surfaces, the structure of this group （as shown in this paper） give rise to the extension of the conjecture regarding the structure of those fundamental groups of any surface.