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Geometry of holomorphic vector fields and applications of Gm-actions 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 Riemann-Roch and Hirzebruch for V-equivariant 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. Bialynicki-Birula, Some theorems on actions of algebraic groups, Ann. of Math. 98, 480-497 (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 Gm-actions to linear algebraic groups
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1977
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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 Riemann-Roch and Hirzebruch for V-equivariant 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. Bialynicki-Birula, Some
theorems on actions of algebraic groups, Ann. of Math. 98, 480-497 (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 .
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Genre | |
Type | |
Language |
eng
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Date Available |
2010-02-21
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080138
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.