On the geometry of the singular locus of a codimension one foliation in Pn

• Omegar Calvo-Andrade ^[1] ; Ariel Molinuevo ^[2] ; Federico Quallbrunn ^[3]
  1. [1] Mathematics Research Center

     Mathematics Research Center

     México

     
  2. [2] Universidade Federal do Rio de Janeiro

     Universidade Federal do Rio de Janeiro

     Brasil

     
  3. [3] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 3, 2019, págs. 857-876
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We will work with codimension one holomorphic foliations over the complex projective space, represented by integrable forms ω∈H0(Ω1Pn(e)). Our main result is that, under suitable hypotheses, the Kupka set of the singular locus of ω∈H0(Ω1P3(e)), defined algebraically as a scheme, turns out to be arithmetically Cohen–Macaulay. As a consequence, we prove the connectedness of the Kupka set in Pn, and the splitting of the tangent sheaf of the foliation, provided that it is locally free.