Title: Discriminants of complete intersection space curves,
Abstract: In this paper, we develop a new approach to the discrimi-nant of a complete
intersection curve in the 3-dimensional projective space. By relying on the
resultant theory, we first prove a new formula that allows us to define this
discrimi-nant without ambiguity and over any commutative ring, in particular in
any characteristic. This formula also provides a new method for evaluating and
computing this discrimi-nant efficiently, without the need to introduce new
variables as with the well-known Cayley trick. Then, we obtain new properties
and computational rules such as the covariance and the invariance formulas.
Finally, we show that our definition of the discriminant satisfies to the
expected geometric property and hence yields an effective smoothness criterion
for complete intersection space curves. Actually, 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.