On generically non-reduced components of Hilbert schemes of smooth curves
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2014
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| _version_ | 1866909470267801600 |
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| author | Dan, Ananyo |
| author_facet | Dan, Ananyo |
| contents | A classical example of Mumford gives a generically non-reduced component of the Hilbert scheme of smooth curves in the projective 3-space such that a general element of the component is contained in a smooth cubic hypersurface in the projective 3-space. In this article we use techniques from Hodge theory to give further examples of such (generically non-reduced) components of Hilbert schemes of smooth curves without any restriction on the degree of the hypersurface containing it. As a byproduct we also obtain generically non-reduced components of certain Hodge loci. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1409_6012 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | On generically non-reduced components of Hilbert schemes of smooth curves Dan, Ananyo Algebraic Geometry 14C30, 14D07, 13D10 A classical example of Mumford gives a generically non-reduced component of the Hilbert scheme of smooth curves in the projective 3-space such that a general element of the component is contained in a smooth cubic hypersurface in the projective 3-space. In this article we use techniques from Hodge theory to give further examples of such (generically non-reduced) components of Hilbert schemes of smooth curves without any restriction on the degree of the hypersurface containing it. As a byproduct we also obtain generically non-reduced components of certain Hodge loci. |
| title | On generically non-reduced components of Hilbert schemes of smooth curves |
| topic | Algebraic Geometry 14C30, 14D07, 13D10 |
| url | https://arxiv.org/abs/1409.6012 |