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EnglishLet $k$ be an algebraically closed field of characteristic $0$ and let $\Hilb_{d}^{G}(\p{N})$ be the open locus of the Hilbert scheme $\Hilb_{d}(\p{N})$ corresponding to Gorenstein subschemes. We proved in several previous papers that $\Hilb_{d}^{G}(\p{N})$ is irreducible for $d\le10$ and $N\ge1$, characterizing its singular locus. In the present paper we prove that also $\Hilb_{11}^{G}(\p{N})$ is irreducible for each $N\ge1$. We also give some results about its singular locus.
http://hdl.handle.net/11583/2577147| Titolo: | On the Gorenstein locus of the punctual Hilbert scheme of degree 11 |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Abstract: | Let $k$ be an algebraically closed field of characteristic $0$ and let $\Hilb_{d}^{G}(\p{N})$ be the open locus of the Hilbert scheme $\Hilb_{d}(\p{N})$ corresponding to Gorenstein subschemes. We proved in several previous papers that $\Hilb_{d}^{G}(\p{N})$ is irreducible for $d\le10$ and $N\ge1$, characterizing its singular locus. In the present paper we prove that also $\Hilb_{11}^{G}(\p{N})$ is irreducible for each $N\ge1$. We also give some results about its singular locus. |
| Digital Object Identifier (DOI): | 10.1016/j.jpaa.2014.01.004 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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