On the geometry of the singular locus of a codimension one foliation in
Omegar Calvo-AndradeCentro de Investigación en Matemáticas, A.C., Guanajuato, Mexico
Ariel MolinuevoUniversidade Federal do Rio de Janeiro, Brazil
Federico QuallbrunnUniversidad de Buenos Aires, Argentina
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. 857–876DOI 10.4171/RMI/1073