Timeline for Smooth algebraic varieties with smooth Kahler quotients.
Current License: CC BY-SA 2.5
12 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Feb 15, 2011 at 8:33 | vote | accept | Dmitri Panov | ||
| Feb 15, 2011 at 8:33 | answer | added | Dmitri Panov | timeline score: 5 | |
| Sep 1, 2010 at 6:22 | comment | added | Dmitri Panov | Well, in this question I make the guess -- that for a "generic" variety with infinite fundamental group its universal cover is not algebraic. Namely that if the fundamental group of the vairety is not virtually abelian, then the universal cover is not algebraic. For plenty of moduli spaces their fundamental group is not virtually ableian (in particular for the moduli spaces of quintics). If what I ask were correct, this would say that Teichmuller space is not algebraic (and hence surely can not be toric). This is the realtion. | |
| Sep 1, 2010 at 2:14 | comment | added | Mohammad Farajzadeh-Tehrani | How your question is related to mathoverflow.net/questions/36388/…? | |
| Aug 23, 2010 at 22:06 | comment | added | Mohan Ramachandran | My earlier comment was wrong so I deleted it.There are examples of compact kahler manifolds with nilpotent fundamental groups due to Campana and Carlson-Toledo.Their universal cover maybe an algebraic variety. | |
| Aug 23, 2010 at 21:24 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Aug 23, 2010 at 16:17 | comment | added | damiano | @Torsten: thanks for the answer! I was indeed stuck on proving that the quotient was Kaehler. I still think that "nilpotent" might be a better fit than "virtually abelian"... | |
| Aug 23, 2010 at 16:15 | comment | added | Torsten Ekedahl | Damiano: Your construction (for matrices of size at least $3\times 3$) gives a non-Kähler variety (it has non-closed 1-forms). | |
| Aug 23, 2010 at 15:57 | comment | added | damiano | I am not sure that this is correct, but have you tried upper triangular matrices over the complex numbers, divided out by the action of the upper triangular matrices with entries in $\mathbb{Z}[i]$? | |
| Aug 23, 2010 at 15:36 | history | edited | Dmitri Panov | CC BY-SA 2.5 |
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| Aug 23, 2010 at 14:58 | history | asked | Dmitri Panov | CC BY-SA 2.5 |