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On the Hodge conjecture for quasi-smooth intersections in toric varieties

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Autor(es):
Bruzzo, Ugo [1, 2, 3, 4, 5] ; Montoya, William [6]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] IGAP Inst Geometry & Phys, Trieste - Italy
[2] INFN Ist Nazl Fis Nucl, Sez Trieste, Trieste - Italy
[3] Arnold Regge Ctr Algebra Geometry & Theoret Phys, Turin - Italy
[4] SISSA Scuola Int Studi Avanzati, Via Bonomea 265, I-34136 Trieste - Italy
[5] Univ Fed Paraiba, Dept Matemat, Campus 1, BR-58051900 Joao Pessoa, Paraiba - Brazil
[6] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP - Brazil
Número total de Afiliações: 6
Tipo de documento: Artigo Científico
Fonte: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; JUL 2021.
Citações Web of Science: 0
Resumo

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 Bruzzo and Grassi (Commun Anal Geom 28: 1773-1786, 2020). 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, under the assumption that the ambient variety P-Sigma(2k+1) has Picard group Z. This extends to a class of toric varieties Otwinowska's result in Otwinowska (J Alg Geom 12: 307-320, 2003). (AU)

Processo FAPESP: 19/23499-7 - Teoria de Noether-Lefschetz em variedades tóricas
Beneficiário:William Daniel Montoya Cataño
Linha de fomento: Bolsas no Brasil - Pós-Doutorado