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.
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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