Timeline for Varieties with an ample vector bundle mapping to their tangent bundle
Current License: CC BY-SA 3.0
20 events
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| Jan 21, 2018 at 20:53 | vote | accept | Daniel Litt | ||
| Jan 21, 2018 at 20:53 | answer | added | Daniel Litt | timeline score: 4 | |
| Aug 22, 2015 at 16:35 | answer | added | P.J | timeline score: 0 | |
| S Aug 20, 2015 at 18:35 | history | bounty ended | CommunityBot | ||
| S Aug 20, 2015 at 18:35 | history | notice removed | CommunityBot | ||
| Aug 17, 2015 at 18:48 | history | edited | Daniel Litt | CC BY-SA 3.0 |
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| Aug 16, 2015 at 19:00 | history | edited | Daniel Litt | CC BY-SA 3.0 |
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| S Aug 12, 2015 at 17:20 | history | bounty started | Daniel Litt | ||
| S Aug 12, 2015 at 17:20 | history | notice added | Daniel Litt | Authoritative reference needed | |
| Aug 12, 2015 at 17:18 | history | edited | Daniel Litt | CC BY-SA 3.0 |
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| Aug 11, 2015 at 13:01 | answer | added | pgraf | timeline score: 6 | |
| Aug 10, 2015 at 19:21 | comment | added | Daniel Litt | ...someone would know a reference off the top of their head, since this question showed up very naturally in something else I've been thinking about recently. | |
| Aug 10, 2015 at 19:21 | comment | added | Daniel Litt | @JasonStarr: I have indeed been looking at these papers. There are several minor issues (for example, I don't immediately see how to show that there is an unsplit family of rational curves in $X$, the first lemma in Andreatta-Wisniewski) which I think I now know how to deal with mostly. The main issue is the application of Lemma 1.2 of Campana-Peternell (arxiv.org/pdf/math/9607217.pdf), which I don't see how to improve to the case of a map which is not generically injective. But I am pretty new to this area, so I could just be missing something easy. In any case, I was hoping... | |
| Aug 10, 2015 at 11:31 | comment | added | Jason Starr | Also, you might look at the articles of S'andor Kov'acs, Carolina Araujo, Stephane Druel, et al. They generalize Andreatta-Wisniewski in various ways. They may address your question. | |
| Aug 10, 2015 at 11:30 | comment | added | Jason Starr | Can you point to a place in the article of Andreatta-Wisniewski where it is necessary for the sheaf homomorphism to be generically injective (as opposed to generically nonzero)? I realize that they state their result only for generically injective homomorphisms, but I do not immediately see a place where this is necessary. | |
| Aug 10, 2015 at 4:49 | history | edited | Daniel Litt | CC BY-SA 3.0 |
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| Aug 10, 2015 at 0:23 | comment | added | Ben Webster♦ | @J.C.Ottem Thanks for the clarification. If Grassmannians don't work, it seems hard to imagine anything else would. | |
| Aug 9, 2015 at 13:59 | comment | added | J.C. Ottem | @BenWebster The tensor product of two ample vector bundles is again ample, yet the only variety with ample tangent bundle is $P^n$. For the Grassmannian, the tangent bundle is however globally generated, for the reason you mentioned. | |
| Aug 9, 2015 at 12:58 | comment | added | Ben Webster♦ | I honestly don't understand the definitions well enough to be sure, but other Grassmannians seem like a good target; their tangent bundles are the tensor product of two bundles which I think are ample. | |
| Aug 9, 2015 at 1:56 | history | asked | Daniel Litt | CC BY-SA 3.0 |