The Complete Intersection Discrepancy of a Curve I: Numerical Invariants

We generalize two classical formulas for complete intersection curves by introducing the the complete intersection discrepancy of a curve as a correction term. The first is a well-known multiplicity formula in singularity theory, due to Lê, Greuel and Teissier, which relates some of the basic invariants of a curve singularity. We apply this generalization elsewhere to the study of equisingularity of curves. The second is the genus–degree formula for projective curves. The main technical tool used to obtain these generalizations is an adjunction-type identity derived from Grothendieck duality theory.