Codimension one distributions and stable rank 2 reflexive sheaves on threefolds

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 mo...

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Bibliographic Details
Published in:Anais da Academia Brasileira de Ciências 2021-01, Vol.93 (suppl 3), p.e20190909-e20190909
Main Authors: CALVO-ANDRADE, OMEGAR, CORRÊA, MAURÍCIO, JARDIM, MARCOS
Format: Article
Language:English
Subjects:
distributions
foliations
moduli spaces
MULTIDISCIPLINARY SCIENCES
reflexive sheaves
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Summary: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 $\sG$ is a subfoliation of a codimension one distribution $\sF$ with isolated singularities, then $\sing(\sG)$ is a curve. As a consequence, we give a criterion to decide whether $\sG$ is globally given as the intersection of $\sF$ 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.
ISSN:0001-3765
1678-2690
1678-2690
DOI:10.1590/0001-3765202120190909