Foliations by curves on threefolds |
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Authors: | Alana Cavalcante Marcos Jardim Danilo Santiago |
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Institution: | 1. UFV, Department of Mathematics, Viçosa-MG, Brazil;2. UNICAMP, Department of Mathematics, Campinas-SP, Brazil;3. IFS, Campus Glória, Nossa Senhora da Glória-SE, Brazil |
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Abstract: | 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 μ-stable whenever the tangent bundle is stable, and apply this fact to the characterization of certain irreducible components of the moduli space of rank 2 reflexive sheaves on and on a smooth quadric hypersurface . Finally, we give a classification of local complete intersection foliations, that is, foliations with locally free conormal sheaves, of degree 0 and 1 on Q3. |
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Keywords: | generic foliations holomorphic distributions moduli spaces stable vector bundles |
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