On the Hodge conjecture for quasi-smooth intersections in toric varieties
| Autor: | Bruzzo, Ugo, Montoya, William D. |
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| Rok vydání: | 2021 |
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| Zdroj: | S\~ao Paulo J. Math. Sci. 15 (2021) 682-694 |
| Druh dokumentu: | Working Paper |
| Popis: | We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we study quasi-smooth intersections in a projective simplicial toric variety, which is a suitable notion to generalize smooth complete intersection subvarieties in the toric environment, and in particular quasi-smooth hypersurfaces. We show that under appropriate conditions, the Hodge Conjecture holds for a very general quasi-smooth intersection subvariety, generalizing the work on quasi-smooth hypersurfaces of the first author and Grassi in [3]. We also show that the Hodge Conjecture holds asymptotically for suitable quasi-smooth hypersurface in the Noether-Lefschetz locus, where "asymptotically" means that the degree of the hypersurface is big enough. This extendes to toric varieties Otwinowska's result in [15]. Comment: 13 pages |
| Databáze: | arXiv |
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