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

  • Omegar Calvo-Andrade

    Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico
  • Ariel Molinuevo

    Universidade Federal do Rio de Janeiro, Brazil
  • Federico Quallbrunn

    Universidad de Buenos Aires, Argentina
On the geometry of the singular locus of a codimension one foliation in $\mathbb P^n$ cover
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Abstract

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

Cite this article

Omegar Calvo-Andrade, Ariel Molinuevo, Federico Quallbrunn, On the geometry of the singular locus of a codimension one foliation in . Rev. Mat. Iberoam. 35 (2019), no. 3, pp. 857–876

DOI 10.4171/RMI/1073