An asymptotic description of the Noether-Lefschetz components in toric varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866912490892296192 |
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| author | Bruzzo, Ugo Montoya, William D. |
| author_facet | Bruzzo, Ugo Montoya, William D. |
| contents | We extend the definition of Noether-Leschetz components to quasi-smooth hypersurfaces in a projective simplicial toric variety of dimension 2k+1, and prove that asymptotically the components whose codimension is upper bounded by a suitable effective constant correspond to hypersurfaces with which one can associate a small degree k-dimensional subvariety. As a corollary we get an asymptotic characterization of the components with small codimension, generalizing Otwinowska's work for odd-dimensional projective spaces and Green and Voisin's for projective 3-space. Some tools developed in this paper are a generalization of Green's theorem for simplicial toric varieties, and an extension of the notion of artinian Gorenstein ideal for the Cox ring of a toric variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_01570 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | An asymptotic description of the Noether-Lefschetz components in toric varieties Bruzzo, Ugo Montoya, William D. Algebraic Geometry 14C22, 14J70, 14M25 We extend the definition of Noether-Leschetz components to quasi-smooth hypersurfaces in a projective simplicial toric variety of dimension 2k+1, and prove that asymptotically the components whose codimension is upper bounded by a suitable effective constant correspond to hypersurfaces with which one can associate a small degree k-dimensional subvariety. As a corollary we get an asymptotic characterization of the components with small codimension, generalizing Otwinowska's work for odd-dimensional projective spaces and Green and Voisin's for projective 3-space. Some tools developed in this paper are a generalization of Green's theorem for simplicial toric varieties, and an extension of the notion of artinian Gorenstein ideal for the Cox ring of a toric variety. |
| title | An asymptotic description of the Noether-Lefschetz components in toric varieties |
| topic | Algebraic Geometry 14C22, 14J70, 14M25 |
| url | https://arxiv.org/abs/1905.01570 |