On the restricted sheaf

Authors : Sabahattin BALCI

Pages : 0-0

Doi:10.1501/Commua1_0000000554

View : 16 | Download : 7

Publication Date : 1988-01-01

Article Type : Research Paper

Abstract :Let X be a connected complex analytic naanifold of dimension n with fundamental group |1|, H be the Sbeaf of the fundamental groups över X [1], rinsert ignore into journalissuearticles values(X, H); be the group of the global sections of H över X and [H, H] c H be the Commutator Subsheaf. It is shown that the Commutator Subsheaf [H, H] insert ignore into journalissuearticles values(or equivalently the Commutator subgroup rinsert ignore into journalissuearticles values(X, [H, H]); of rinsert ignore into journalissuearticles values(X, H);); determines the Restricted Sheaf A of germs of holomorphic functions över X [5] and the subsheaves of H defined by the normal subgroups of rinsert ignore into journalissuearticles values(X, H); such that they ccntain [H, H] insert ignore into journalissuearticles values(or the normal subgroups of rinsert ignore into journalissuearticles values(X, H); such that they contain rinsert ignore into journalissuearticles values(X, [H, H]);); determine the Restric­ ted ideal Sheaves of the sheaf A [6]. In addition, the subsheaves of H insert ignore into journalissuearticles values(or the normal subgroups of r insert ignore into journalissuearticles values(X, H););, which determine the Restricted ideal Sheaves, satisfy the descending insert ignore into journalissuearticles values(minimal); chain condition. Fiually, the Commutator Subgroup F insert ignore into journalissuearticles values(X, [H, H]); completely determines the vector space A insert ignore into journalissuearticles values(X); of holomorphic functions on X.
Keywords : restricted sheaf, Mathematics, Statistics