Codimension one distributions and stable rank 2 reflexive sheaves on threefolds

Author(s)

Calvo-Andrade, Omegar ^[1] ; Correa, Mauricio ^[2] ; Jardim, Marcos ^[3]

Affiliation

^[1] CIMAT, Ctr Invest Matemat, Ap Postal 402, Guanajuato 36000, Gto - Mexico

^[2] ICEX UFMG, Dept Matemat, Av Antonio Carlos 6627, BR-31270901 Belo Horizonte, MG - Brazil

^[3] IMECC UNICAMP, Dept Matemat, Rua Sergio Buarque Holanda 651, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: Anais da Academia Brasileira de Ciências; v. 93, n. 3 2021.
• Web of Science Citations: 0

Abstract

We show that codimension one distributions with at most isolated singularities on certain smooth projective threefolds with Picard rank one have stable tangent sheaves. The ideas in the proof of this fact are then applied to the characterization of certain irreducible components of the moduli space of stable rank 2 reflexive sheaves on P3, and to the construction of stable rank 2 reflexive sheaves with prescribed Chern classes on general threefolds. We also prove that if G is a subfoliation of a codimension one distribution F with isolated singularities, then Sing (G) is a curve. As a consequence, we give a criterion to decide whether G is globally given as the intersection of F with another codimension one distribution. Turning our attention to codimension one distributions with non isolated singularities, we determine the number of connected components of the pure 1-dimensional component of the singular scheme. (AU)

• FAPESP's process: 18/21391-1 - Gauge theory and algebraic geometry
• Grantee: Marcos Benevenuto Jardim
• Support Opportunities: Research Projects - Thematic Grants