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Geometry of holomorphic vector fields and applications of Gmactions to linear algebraic groups Akyildiz, Ersan
Abstract
A generalization of a theorem of N.R. 0'Brian, zeroes of holomorphic vector fields and the Grothendieck residue, Bull. London Math. Soc, 7 (1975) is given. The theorem of RiemannRoch and Hirzebruch for Vequivariant holomorphic vector bundles is obtained, via holomorphic vector fields, in the case all zeroes of the holomorphic vector field V are isolated. The Bruhat decomposition of G/B is obtained from the G action on G/B . It is shown that a theorem of A. BialynickiBirula, Some theorems on actions of algebraic groups, Ann. of Math. 98, 480497 (1973) is the generalization of the Bruhat decomposition on G/B , which was a conjecture of B. Iversen. The existence of a G action on G/P with only one fixed a point is proved, where G is a connected linear algebraic group defined over an algebraically closed field k of characteristic zero and P is a parabolic subgroup of G . The following is obtained P = N[sub G](Pu) = {geG: Adg(Pu) = Pu} where G is a connected linear algebraic group, P is a parabolic subgroup of G and P^ is the tangent space of the set of unipotent elements of P at the identity. An elementary proof of P = N[sub G](P) = {geG: gPg ⁻¹=P} is given, where G is a connected linear algebraic group and P is a parabolic subgroup of G .
Item Metadata
Title 
Geometry of holomorphic vector fields and applications of Gmactions to linear algebraic groups

Creator  
Publisher 
University of British Columbia

Date Issued 
1977

Description 
A generalization of a theorem of N.R. 0'Brian, zeroes of holomorphic vector fields and the Grothendieck residue, Bull. London Math. Soc, 7 (1975) is given.
The theorem of RiemannRoch and Hirzebruch for Vequivariant holomorphic vector bundles is obtained, via holomorphic vector fields, in the case all zeroes of the holomorphic vector field V are isolated.
The Bruhat decomposition of G/B is obtained from the G action on G/B .
It is shown that a theorem of A. BialynickiBirula, Some
theorems on actions of algebraic groups, Ann. of Math. 98, 480497 (1973)
is the generalization of the Bruhat decomposition on G/B , which was
a conjecture of B. Iversen.
The existence of a G action on G/P with only one fixed
a
point is proved, where G is a connected linear algebraic group defined over an algebraically closed field k of characteristic zero and P is a parabolic subgroup of G .
The following is obtained
P = N[sub G](Pu) = {geG: Adg(Pu) = Pu}
where G is a connected linear algebraic group, P is a parabolic subgroup of G and P^ is the tangent space of the set of unipotent elements of P at the identity.
An elementary proof of P = N[sub G](P) = {geG: gPg ⁻¹=P} is given,
where G is a connected linear algebraic group and P is a parabolic subgroup of G .

Genre  
Type  
Language 
eng

Date Available 
20100221

Provider 
Vancouver : University of British Columbia Library

Rights 
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

DOI 
10.14288/1.0080138

URI  
Degree  
Program  
Affiliation  
Degree Grantor 
University of British Columbia

Campus  
Scholarly Level 
Graduate

Aggregated Source Repository 
DSpace

Item Media
Item Citations and Data
Rights
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.