Section: New Results

Discriminant of a complete intersection space curve

Participant : Laurent Busé.

In this work, we develop the formalism of the discriminant of a complete intersection curve in the three dimensional projective space, that is to say a curve which is represented as the zero locus of two homogeneous polynomials in four variables. Our main objective is to provide a new computational approach to this object without relying on the so-called "Cayley trick" for which it is necessary to introduce new variables. We also aim at getting a universal definition of this discriminant over the integers so that it holds under any specialization of the coefficients to an arbitrary commutative ring. Another aspect of this work is to explore properties of this discriminant, typically invariance, covariance and change of basis properties.

This is an on going work which is done in collaboration with Ibrahim Nonkane (University of Ouagadougou, Burkina Faso).