Deformation of pairs and Noether-Lefschetz loci in toric varieties
| Autor: | Bruzzo, Ugo, Montoya, William D. |
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| Rok vydání: | 2022 |
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| Druh dokumentu: | Working Paper |
| Popis: | We continue our study of the Noether-Lefschetz loci in toric varieties and investigate deformation of pairs (V,X) where V is a complete intersection subvariety and X a quasi-smooth hypersurface in a odd dimensional simplicial projective toric variety, with V\subset X. Under some assumptions, we prove that the cohomological class in H^{k,k}(X) associated to V remains of type (k,k) under an infinitesimal deformation if and only if V remains algebraic. Actually we prove that locally the Noether-Lefschetz locus is an irreducible component of a suitable Hilbert scheme. This generalizes Theorem 4.2 in our previous work [4] and the main theorem proved by Dan in [10]. Comment: 9 pages. arXiv admin note: text overlap with arXiv:2102.01050 |
| Databáze: | arXiv |
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