Timeline for every abelian scheme quotient of a Picard scheme?
Current License: CC BY-SA 3.0
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| when toggle format | what | by | license | comment | |
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| Feb 14, 2013 at 15:19 | history | edited | user19475 | CC BY-SA 3.0 |
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| Feb 8, 2013 at 19:15 | comment | added | Simon Pepin Lehalleur | $M_{g,n}$ is very far from being affine. For every $g\geq 3$, there is a complete curve passing through any point. This follows from the existence of a compactification with boundary of codimension >1 (the Satake compactification). The problem is only the complement of a very ample divisor is guaranteed to be affine. | |
| Feb 2, 2013 at 16:53 | comment | added | Vivek Shende | also, the complement of a divisor has no reason to be affine -- take $\mathbb{P}^1 \times \mathbb{P}^1 \setminus 0 \times \mathbb{P}^1 = \mathbb{A}^1 \times \mathbb{P}^1$. | |
| Feb 2, 2013 at 11:14 | comment | added | Laurent Moret-Bailly | The Kodaira-Parshin construction produces lots of non-isotrivial proper and smooth curves over a smooth projective curve. See for example M. Martin-Deschamps, Astérisque vol. 127 (1985). | |
| Feb 2, 2013 at 9:51 | history | answered | user19475 | CC BY-SA 3.0 |