On the geometry of the Kupka set of a foliation

ARIEL MOLINUEVO; OMEGAR CALVO-ANDRADE; FEDERICO QUALLBRUNN

Niteroi, Rio de Janeiro

Conferencia; Complex foliations, dynamics and geometry; 2018

Universidade Federal Fluminense

We will work with codimension one holomorphic foliations over the complex projective space, represented by integrable forms ω ∈ H0(Ω1,Pn(e)).Our main result is that, under suitable hypotheses, the Kupka set of the singular locus of ω, defined algebraically as a scheme, turns out to be arithmetically Cohen-Macaulay. As a consequence, we prove the connectedness of the Kupka set, and the splitting of the tangent sheafof the foliation, provided that it is locally free.