The Kupka Scheme and Unfoldings

MASSRI, CESAR; MOLINUEVO, ARIEL; QUALLBRUNN, FEDERICO

ASIAN JOURNAL OF MATHEMATICS

INT PRESS BOSTON, INC

Año: 2018 vol. 22 p. 1025 - 1046

1093-6106

Let w 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 w and the first order unfoldings of w.Exploiting this relation, we show that the set of Kupka points of w is generically not empty.As an application of this results, we can compute the ideal of first order unfoldings for some known components of the space of foliations.