|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
On the stability of flat complex vector bundles over parallelizable manifolds | | Indranil Biswas
; Sorin Dumitrescu
; | | Date: |
18 Sep 2017 | | Abstract: | We investigate the flat holomorphic vector bundles over compact complex
parallelizable manifolds $G / Gamma$, where $G$ is a complex connected Lie
group and $Gamma$ is a cocompact lattice in it. The main result proved here is
a structure theorem for flat holomorphic vector bundles $E_
ho$ associated to
any irreducible representation $
ho ,: ,Gamma ,longrightarrow,
ext{GL}(d, {mathbb C})$. More precisely, we prove that $E_{
ho}$ is
holomorphically isomorphic to a vector bundle of the form $E^{oplus n}$, where
$E$ is a stable vector bundle. All the rational Chern classes of $E$ vanish, in
particular, its degree is zero.
We deduce a stability result for flat holomorphic vector bundles $E_{
ho}$
of rank 2 over compact quotients $ ext{SL}(2, {mathbb C}) / Gamma$. If an
irreducible homomorphism $
ho ,:, Gamma ,longrightarrow, ext{SL}(2,
mathbb {C})$ satisfies the condition that the projection $Gamma,
longrightarrow, {
m PGL}(2, {mathbb C})$, obtained by composing of $
ho$
with the projection of $ ext{SL}(2,{mathbb C})$ to ${
m PGL}(2, {mathbb
C})$, does not extend to $ ext{SL}(2, mathbb {C})$, then $E_{
ho}$ is proved
to be stable. | | Source: | arXiv, 1709.5951 | | 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