Timeline for Moduli space of semistable bundles
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Feb 22, 2020 at 7:20 | vote | accept | Sebastian | ||
| Jun 3, 2018 at 16:20 | history | edited | Sean Lawton | CC BY-SA 4.0 |
added relevant tag.
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| Jun 1, 2018 at 21:28 | history | edited | Qfwfq | CC BY-SA 4.0 |
added 8 characters in body
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| Jun 1, 2018 at 21:14 | answer | added | Sean Lawton | timeline score: 5 | |
| Jul 26, 2010 at 6:20 | comment | added | Sebastian | It depends on your point of view. In the differential geometric setup, the metric is quite natural. The moduli space can be identified with the moduli space of flat SU(2) connections, where the stable bundle correspond to the irreducible connections. The tangent space at some connection A can be identified with the space of harmonic $\phi\in\Omega^1(su(V)).$ This space has a natural metric $\int trace(\phi\wedge*\tilde\phi).$ | |
| Jul 23, 2010 at 18:21 | comment | added | Michael Thaddeus | What natural Riemannian metric are you referring to? I would say that what this moduli space possesses, very naturally, is a complex structure. The questions are then whether the Goldman form v(x,y) -- the natural symplectic form -- extends over the semistable locus where it is not a priori defined, and whether g(x,y) := v(ix,y) is positive definite. If so, since we know v is closed, we would conclude that g is automatically Kähler (see p. 107 of Griffiths & Harris). However, I don't know offhand whether the answers are positive or negative. | |
| Jul 23, 2010 at 12:47 | history | edited | Charles Matthews | CC BY-SA 2.5 |
typo
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| Jul 23, 2010 at 11:43 | comment | added | Pete L. Clark | The word "Bundles" in the title was changed to "vundles". This seems awfully strange to me, but I'll wait for some corroboration that "vundle" is not the hip new term for "vector bundle" before suggesting a rollback. | |
| Jul 23, 2010 at 11:28 | history | edited | Charles Matthews | CC BY-SA 2.5 |
copy edit
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| Jul 23, 2010 at 7:45 | history | asked | Sebastian | CC BY-SA 2.5 |