Timeline for Variations of Hodge structures over the line
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2017 at 4:18 | vote | accept | asv | ||
| Sep 14, 2017 at 23:14 | answer | added | Daniel Litt | timeline score: 9 | |
| Sep 14, 2017 at 14:31 | comment | added | asv | @DanielLitt: Thank you for your interesting comment. Could you state explicitly the theorem of the fixed part? This could be a final answer to my question. | |
| Sep 14, 2017 at 13:09 | comment | added | Daniel Litt | Of course one can make examples; for example, families of del Pezzo surfaces; or one may take $X\times\mathbb{A}^1$ for any $X$ containing a rational curve, so that the map $X\times \mathbb{A}^1\to\mathbb{A}^1$ has a section, and blow up the image of the section. But I don't know any examples with really "interesting" geometry, for the reasons described in my previous comment. | |
| Sep 14, 2017 at 13:07 | comment | added | Daniel Litt | Such a variation of Hodge structure is trivial, by e.g. the theorem of the fixed part, as $\mathbb{A}^1$ is simply connected, so all the Hodge structures are isomorphic. More is true: by work of Viehweg, Moller, Zuo, and others, "most" moduli spaces are hyperbolic, and so contain no $\mathbb{A}^1$'s... | |
| Sep 14, 2017 at 12:31 | comment | added | Piotr Achinger | What is a good example of a nontrivial such family? | |
| Sep 14, 2017 at 11:18 | history | edited | asv | CC BY-SA 3.0 |
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| Sep 14, 2017 at 11:08 | history | asked | asv | CC BY-SA 3.0 |