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Foliations by curves on threefolds

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 نشر من قبل Marcos Jardim
 تاريخ النشر 2021
  مجال البحث
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We study the conormal sheaves and singular schemes of 1-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 $TX$ is stable, and apply this fact to the characterization of certain irreducible components of the moduli space of rank 2 reflexive sheaves on $mathbb{P}^3$ and on a smooth quadric hypersurface $Q_3subsetmathbb{P}^4$. Finally, we give a classification of local complete intersection foliations, that is, foliations with locally free conormal sheaves, of degree 0 and 1 on $Q_3$.



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187 - B.Wang 2017
This is an example on the cohomology of threefolds.
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