Timeline for Threefolds of general type with no holomorphic forms?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Dec 20, 2018 at 15:41 | answer | added | Chen Jiang | timeline score: 7 | |
| Dec 19, 2018 at 9:59 | vote | accept | abx | ||
| Dec 18, 2018 at 21:18 | history | edited | Qfwfq | CC BY-SA 4.0 |
deleted 2 characters in body
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| Dec 18, 2018 at 21:09 | answer | added | Jason Starr | timeline score: 9 | |
| Dec 18, 2018 at 19:54 | comment | added | Sasha | @abx: Sure, but when you take the quotient you can kill higher cohomology groups. At list this is what happens for fake quadrics. | |
| Dec 18, 2018 at 19:47 | comment | added | abx | @Sasha: $\chi (\mathcal{O})$ is negative for a curve, so for a product of $n$ curves it has the same sign as $(-1)^n$. | |
| Dec 18, 2018 at 19:29 | comment | added | Jason Starr | For the pencil of Godeaux surfaces, it looks like the Reid -- Shepherd-Barron -- Tai criterion applies. I will try to write up the details below . . . | |
| Dec 18, 2018 at 19:28 | comment | added | Sasha | @abx: Sorry, but I don't understand why is $\chi(\mathcal{O}) < 0$? In the surface case this objection doesn't work, right? | |
| Dec 18, 2018 at 19:17 | comment | added | abx | @Sasha: Again this would have $\chi (\mathcal{O})<0$. | |
| Dec 18, 2018 at 19:16 | comment | added | Jason Starr | Maybe a general pencil of Godeaux surfaces? . . . | |
| Dec 18, 2018 at 18:34 | comment | added | Sasha | @abx: Isn't it possible to cook up an example by taking the quotient of the product of three curves by a finite group action, an analogue of fake $\mathbb{P}^1 \times \mathbb{P}^1$? | |
| Dec 18, 2018 at 18:07 | comment | added | abx | @Sasha: forms of all degrees $>0$. | |
| Dec 18, 2018 at 18:05 | comment | added | abx | @Jason Starr: no, that doesn't work. $\chi (\mathcal{O})$ is negative for a complete intersection threefold of general type, thus also for any quotient by a free action, while we want $\chi (\mathcal{O})=1$. | |
| Dec 18, 2018 at 17:47 | comment | added | Jason Starr | Presumably there are examples that are quotients of general type 3fold complete intersections similar to the Godeaux surface. Do you want examples that are simply connected? | |
| Dec 18, 2018 at 17:42 | comment | added | Sasha | Forms of some degree, or forms of all degrees? | |
| Dec 18, 2018 at 17:00 | history | asked | abx | CC BY-SA 4.0 |