On the geometry of the singular locus of a codimension one foliation in Pn\mathbb P^n

  • 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
Download PDF

A subscription is required to access this article.

Abstract

We will work with codimension one holomorphic foliations over the complex projective space, represented by integrable forms ωH0(ΩPn1(e))\omega\in H^0(\Omega^1_{\mathbb{P}^n}(e)). Our main result is that, under suitable hypotheses, the Kupka set of the singular locus of ωH0(ΩP31(e))\omega\in H^0(\Omega^1_{{\mathbb{P}}^3}(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\mathbb{P}^n, 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 Pn\mathbb P^n. Rev. Mat. Iberoam. 35 (2019), no. 3, pp. 857–876

DOI 10.4171/RMI/1073