Hilbert Scheme of a Pair of Skew Lines on Cubic Threefolds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866908326206373888 |
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| author | Zhang, Yilong |
| author_facet | Zhang, Yilong |
| contents | A pair of disjoint lines on a smooth cubic threefold determines an irreducible component of the Hilbert scheme. We prove that this component is smooth and isomorphic to the blow-up of the symmetric product of Fano varieties of lines on the diagonal. We also study its relation to the geometry of lines and singularities on the hyperplane sections and its relation to Bridgeland moduli spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_11622 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hilbert Scheme of a Pair of Skew Lines on Cubic Threefolds Zhang, Yilong Algebraic Geometry 14C05, 14J30 A pair of disjoint lines on a smooth cubic threefold determines an irreducible component of the Hilbert scheme. We prove that this component is smooth and isomorphic to the blow-up of the symmetric product of Fano varieties of lines on the diagonal. We also study its relation to the geometry of lines and singularities on the hyperplane sections and its relation to Bridgeland moduli spaces. |
| title | Hilbert Scheme of a Pair of Skew Lines on Cubic Threefolds |
| topic | Algebraic Geometry 14C05, 14J30 |
| url | https://arxiv.org/abs/2010.11622 |