Foliations by curves on threefolds

Autor(es)

Cavalcante, Alana ; Jardim, Marcos ; Santiago, Danilo

• Tipo de documento: Artigo Científico
• Fonte: Mathematische Nachrichten; v. 296, n. 2, p. 22-pg., 2023-02-01.

Resumo

We study the conormal sheaves and singular schemes of one-dimensional foliations on smooth projective varieties X of dimension 3 and Picard rank 1. We prove that if the singular scheme has dimension 0, then the conormal sheaf is mu-stable whenever the tangent bundle TX$TX$ is stable, and apply this fact to the characterization of certain irreducible components of the moduli space of rank 2 reflexive sheaves on P3$\mathbb {P}<^>3$ and on a smooth quadric hypersurface Q3 subset of P4$Q_3\subset \mathbb {P}<^>4$. Finally, we give a classification of local complete intersection foliations, that is, foliations with locally free conormal sheaves, of degree 0 and 1 on Q(3). (AU)

• Processo FAPESP: 18/21391-1 - Teoria de calibre e geometria algébrica
• Beneficiário: Marcos Benevenuto Jardim
• Modalidade de apoio: Auxílio à Pesquisa - Temático