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

Omegar Calvo Andrade, Ariel Molinuevo, Federico Quallbrunn

• 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.