Timeline for does there exist a family of objects over the tangent space to the base space of a family of objects?
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7 events
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| Feb 11, 2013 at 13:17 | vote | accept | IMeasy | ||
| Feb 7, 2013 at 23:05 | comment | added | Piotr Achinger | What I think Dan meant is: if the families you are considering are families of elliptic curves with fixed basis of $n$-torsion, the moduli space will be the modular curve $X(n)$ (or rather its open subset $Y(n)$). After removing finitely many points, it will be a fine moduli space. As computed here en.wikipedia.org/wiki/Modular_curve , the genus of $X(n)$ is nonzero for most $n$. Since $X(n)$ is smooth, for such $n$ there are no non-constant maps $\mathbb{A}^1\to X(n)$, that is, every family of the considered type over $\mathbb{A}^1$ has to be constant. | |
| Feb 6, 2013 at 18:19 | comment | added | IMeasy | thank you two! @Dan: could you develop your example a little more? | |
| Feb 6, 2013 at 17:53 | comment | added | Dan Petersen | For an example, take the modular curve $X(n)$ (with $n$ not too small). | |
| Feb 6, 2013 at 16:19 | history | edited | Piotr Achinger | CC BY-SA 3.0 |
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| Feb 6, 2013 at 16:12 | history | edited | Piotr Achinger | CC BY-SA 3.0 |
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| Feb 6, 2013 at 16:04 | history | answered | Piotr Achinger | CC BY-SA 3.0 |