The Complete Intersection Discrepancy of a Curve I: Numerical Invariants

Abstract: We generalize two classical formulas for complete intersection curves using the complete intersection discrepancy of a curve as a correction term. The first formula is a well-known multiplicity formula in singularity theory due to L^e, Greuel and Teissier that relates some of the basic invariants of a curve singularity. We apply its generalization elsewhere to the study of equisingularity of curves. The second formula 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.