Asian Journal of Mathematics
Volume 22 (2018)
The Kupka scheme and unfoldings
Pages: 1025 – 1046
Let $\omega$ be a differential $1$-form defining an algebraic foliation of codimension 1 in projective space. In this article we use commutative algebra to study the singular locus of $\omega$ through its ideal of definition. Then, we expose the relation between the ideal defining the Kupka components of the singular set of $\omega$ and the first order unfoldings of $\omega$. Exploiting this relation, we show that the set of Kupka points of $\omega$ is generically not empty.
As an application of these results, we can compute the ideal of first order unfoldings for some known components of the space of foliations.
Kupka singularities, foliation, unfoldings
2010 Mathematics Subject Classification
The authors were fully supported by CONICET, Argentina.
Received 15 December 2015
Accepted 16 February 2017
Published 6 February 2019