Deformation of pairs and Noether-Lefschetz loci in toric varieties

Ugo Bruzzo; William D. Montoya

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arXiv · 2203.00664

Deformation of pairs and Noether-Lefschetz loci in toric varieties

Ugo Bruzzo·William D. Montoya

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Abstract

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].

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BibTeX RIS

Ugo Bruzzo, William D. Montoya. 2022-03-01. Deformation of pairs and Noether-Lefschetz loci in toric varieties. https://arxiv.org/abs/2203.00664

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