|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry | | Laurent Bruasse
; Andrei Teleman
; | | Date: |
19 Sep 2003 | | Subject: | Complex Variables; Symplectic Geometry; Algebraic Geometry; Differential Geometry MSC-class: 32M05; 53D20; 14L24; 14L30; 32L05; 32Q15 | math.CV math.AG math.DG math.SG | | Abstract: | We give a generalisation of the theory of optimal destabilizing 1-parameter subgroups to non-algebraic complex geometry. Consider a holomorphic action $G imes F o F$ of a complex reductive Lie group $G$ on a finite dimensional (possibly non-compact) Kähler manifold $F$. Using a Hilbert type criterion for the (semi)stability of symplectic actions, we associate to any non semistable point $fin F$ a unique optimal destabilizing vector in $g$ and then a naturally defined point $f_0$ which is semistable for the action of a certain reductive subgroup of $G$ on a submanifold of $F$. We get a natural stratification of $F$ which is the analogue of the Shatz stratification for holomorphic vector bundles. In the last chapter we show that our results can be generalized to the gauge theoretical framework: first we show that the system of semistable quotients associated with the classical Harder-Narasimhan filtration of a non-semistable bundle $EE$ can be recovered as the limit object in the direction given by the optimal destabilizing vector of $EE$. Second, we extend this principle to holomorphic pairs: we give the analogue of the Harder-Narasimhan theorem for this moduli problem and we discuss the relation between the Harder-Narasimhan filtration of a non-semistable holomorphic pair and its optimal destabilizing vector. | | Source: | arXiv, math.CV/0309315 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER