On fundamental groups related to the Hirzebruch surface F_1  

作　　者：Michael FRIEDMAN Mina TEICHER 

机构地区：[1]Department of Mathematics,Bar-Ilan University

出　　处：《Science China Mathematics》2008年第4期728-745,共18页中国科学：数学（英文版）

基　　金：This work was supported by the Emmy Noether Institute Fellowship(by the Minerva Foundation of Germany);Israel Science Foundation(Grant No.8008/02-3)

摘　　要：Given a projective surface and a generic projection to the plane,the braid monodromy factorization(and thus,the braid monodromy type)of the complement of its branch curve is one of the most important topological invariants,stable on deformations.From this factorization,one can compute the fundamental group of the complement of the branch curve,either in C^2 or in CP^2.In this article,we show that these groups,for the Hirzebruch surface F_1,(a,b),are almost-solvable.That is, they are an extension of a solvable group,which strengthen the conjecture on degeneratable surfaces.Given a projective surface and a generic projection to the plane,the braid monodromy factorization（and thus,the braid monodromy type）of the complement of its branch curve is one of the most important topological invariants,stable on deformations.From this factorization,one can compute the fundamental group of the complement of the branch curve,either in C² or in CP².In this article,we show that these groups,for the Hirzebruch surface F₁,（a,b）,are almost-solvable.That is, they are an extension of a solvable group,which strengthen the conjecture on degeneratable surfaces.

关 键 词：Hirzebruch SURFACES DEGENERATION generic PROJECTION branch curve BRAID MONODROMY FUNDAMENTAL group classification of SURFACES 

分 类 号：O152[理学—数学]