Timeline for Positive vector bundles
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2011 at 23:27 | answer | added | diverietti | timeline score: 6 | |
| Apr 27, 2010 at 9:11 | answer | added | Henri | timeline score: 3 | |
| Apr 26, 2010 at 22:51 | comment | added | Charles Siegel | I'm going to second recommending Lazarsfeld, and toss out Hartshorne's "Ample Subvarieties of Algebraic Varieties." | |
| Apr 26, 2010 at 22:01 | answer | added | Vamsi | timeline score: 4 | |
| Nov 13, 2009 at 7:46 | history | edited | Csar Lozano Huerta | CC BY-SA 2.5 |
I edit the question because the previous one was ambiguous.; added 3 characters in body
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| Nov 7, 2009 at 7:07 | comment | added | Csar Lozano Huerta | I have in mind the following definition. Let E be a holomorphic vector bundle over M with a hermitian metric. Moreover let D be a connection on E. Then we can define D^2 so that the curvature matrix of 2-forms. Such a curvature matrix (tensor) gives rise to a Hermitian form O_E on the bundle TM\otimes E. We can say that E is positive if such a hermitian form O_E is positive at every point of M. | |
| Nov 7, 2009 at 1:05 | comment | added | Ryan Budney | Perhaps your question isn't specific enough. What do you mean by "curvature" for a general vector bundle? | |
| Nov 6, 2009 at 16:58 | comment | added | Csar Lozano Huerta | Let's say that a vector bundle E is positive if its curvature form is positive everywhere. What is the geometric info about our manifold that this fact carries? | |
| Nov 6, 2009 at 15:31 | answer | added | S. Carnahan♦ | timeline score: 6 | |
| Nov 6, 2009 at 15:22 | comment | added | 1-- | I'm not sure if this helps, but when I hear 'positive vector bundle', I think of something along the lines of eom.springer.de/p/p073980.htm. Anyway, it would be good to know what Csar has in mind exactly. | |
| Nov 6, 2009 at 11:22 | comment | added | David E Speyer | I believe there is a definition of positivity of a vector bundle in Lazarsfeld's book "Positivity in Algebraic Geometry." That said, I would also like to know what defnition Csar is using. | |
| Nov 6, 2009 at 7:21 | comment | added | Kim Morrison | I don't understand what sense of positivity you're talking about here. | |
| Nov 6, 2009 at 6:29 | history | asked | Csar Lozano Huerta | CC BY-SA 2.5 |