Codimension one distributions and stable rank 2 reflexive sheaves on threefolds

2018/12/29 by Calvo-Andrade, Omegar, Corrêa, Maurício, Jardim, Marcos
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.11355

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 \mathscrG is a subfoliation of a codimension one distribution \mathscrF with isolated singularities, then Sing(\mathscrG) is a curve. As a consequence, we give a criterion to decide whether \mathscrG is globally given as the intersection of \mathscrF 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.

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• On the connectedness of the singular set of holomorphic foliations

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• Codimension one distributions of degree 3 on the three-dimensional projective space
• Moduli of Reflexive Sheaves on Smooth Projective 3-folds
• Rank two sheaves with maximal third Chern character in three-dimensional\n projective space
• Foliations by curves on threefolds
• Distributions with locally free tangent sheaf