On the restricted sheaf

Year 1988, Volume: 37 , - , 01.01.1988

Sabahattin Balcı

https://doi.org/10.1501/Commua1_0000000554

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], r(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] (or equivalently the Commutator subgroup r(X, [H, H]) of r(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 r(X, H) such that they ccntain [H, H] (or the normal subgroups of r(X, H) such that they contain r(X, [H, H])) determine the Restric­ ted ideal Sheaves of the sheaf A [6]. In addition, the subsheaves of H (or the normal subgroups of r (X, H)), which determine the Restricted ideal Sheaves, satisfy the descending (minimal) chain condition.
Fiually, the Commutator Subgroup F (X, [H, H]) completely determines the vector space A (X) of holomorphic functions on X.

Keywords

restricted sheaf, Mathematics, Statistics

References

• Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi