Timeline for Rationality of Hilbert schemes?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 30, 2016 at 9:25 | comment | added | Jason Starr | In fact $H_{0,3}$ is rational. This is easier to see if you use the space of stable maps of degree $e$, genus $0$ curves to $\mathbb{P}^n$, say $\overline{\mathcal{M}}_{0,0}(\mathbb{P}^n,e)$. Then the standard torus action on $\mathbb{P}^n$ induces a torus action on the space of stable maps. Using Bialynicki-Birula, you are reduced to showing rationality of certain fixed point loci; for $e=3$, the fixed point loci are just points. Herb Clemens has a paper about this. | |
| Dec 30, 2016 at 5:01 | vote | accept | Elle Najt | ||
| Dec 30, 2016 at 4:36 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
Fix $...$ $...$ infelicity
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| Dec 30, 2016 at 3:52 | history | edited | Noam D. Elkies | CC BY-SA 3.0 |
fix typo: embedded with degree d, not 3.
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| Dec 30, 2016 at 3:35 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |