Discriminants of complete intersection space curves

In this talk we will present a new approach to the discriminant of a complete intersection curve in the 3-dimensional projective space. By relying on the resultant theory, we prove a new formula that allows us to define this discriminant without ambiguity and over any commutative ring, in particular in any characteristic.This formula also provides a new method for evaluating and computing this discriminant more efficiently, without the need to introduce new variables as with the well-known Cayley trick. Then, we derive new properties and we show that this new definition of the discriminant satifises to the expected geometric property and hence yields an effective smoothness criterion for complete intersection space curves. More precisely, we show that in the generic setting, it is the defining equation of the discriminant scheme if the ground ring is assumed to be a unique factorization domain.