Logarithmic forms and singular projective foliations

Abstract

In this article we describe formulas for regular projective logarithmic $q$-forms and characterize those that define singular foliations of codimension $q$ in a projective space. The main result is the proof of their infinitesimal stability when $q=2$ with some extra degree assumptions. This work allows us to determine new irreducible components of the corresponding moduli space of codimension two singular projective foliations of a fixed degree, which are also generically reduced according to its scheme structure. We also set the background to extend these results to the case $2 \le q\le n-2$.