Timeline for Moduli of coherent sheaves on abelian varieties
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| S Dec 22, 2015 at 10:04 | history | bounty ended | CommunityBot | ||
| S Dec 22, 2015 at 10:04 | history | notice removed | CommunityBot | ||
| Dec 14, 2015 at 12:19 | comment | added | Bernie | Have you had a look at "Geometry of the moduli spaces of sheaves" by Huybrechts and Lehn? They construct these coarse moduli spaces for polarized projective schemes. They also construct a relative version: a coarse moduli scheme for sheaves on the fibers of a projective morphisms with a relative ample line bundle. Maybe this is a good starting point, see ncatlab.org/nlab/files/HuybrechtsLehn.pdf | |
| S Dec 14, 2015 at 8:40 | history | bounty started | gradstudent | ||
| S Dec 14, 2015 at 8:40 | history | notice added | gradstudent | Authoritative reference needed | |
| Dec 14, 2015 at 8:40 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Dec 14, 2015 at 6:19 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Dec 10, 2015 at 14:29 | comment | added | gradstudent | Prof. @JasonStarr, and when you said there is a projective coarse moduli space of semistable objects, is that for a single $(A,\theta)$ or is it over $\mathcal{A}_g$? | |
| Dec 10, 2015 at 13:44 | history | edited | gradstudent | CC BY-SA 3.0 |
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| Dec 10, 2015 at 13:44 | comment | added | gradstudent | I am sorry, I meant the universal sheaf only! | |
| Dec 10, 2015 at 13:18 | comment | added | Jason Starr | Even for a single $(A,\theta)$, there is not a moduli scheme $\mathcal{M}(r,c_i)$ for that $A$. There is an Artin stack. If you specify a stability condition, there is frequently a projective coarse moduli space of semistable objects. Also, if memory serves, the Brauer group of $\mathcal{A}_g$ equals $\mathbb{Q}/\mathbb{Z}$ (I think I proved that here some years ago). Since this is nontrivial, likely there do not exist universal sheaves over those coarse moduli spaces (I am not sure why you refer to such a universal sheaf as a Poincare "line bundle). | |
| Dec 10, 2015 at 1:22 | history | asked | gradstudent | CC BY-SA 3.0 |