Foliations with persistent singularities

MASSRI, CÉSAR; MOLINUEVO, ARIEL; QUALLBRUNN, FEDERICO

JOURNAL OF PURE AND APPLIED ALGEBRA

ELSEVIER SCIENCE BV

Año: 2020 vol. 225

0022-4049

Let $omega$ be a differential $q$-form defining a foliation of codimension $q$ in a projective variety.In this article we study the singular locus of $omega$ in various settings. We relate a certain type of singularities, which we name emph{persistent}, with the unfoldings of $omega$, generalizing previous work done on foliations of codimension $1$ in projective space. We also relate the absence of persistent singularities with the existence of a connection in the sheaf of $1$-forms defining the foliation. In the latter parts of the article we extend some of these results to toric varieties by making computations on the Cox ring and modules over this ring.p, li { white-space: pre-wrap; }