The Complete Intersection Discrepancy of a Curve I: Numerical Invariants

2025/04/12 by Andrei Benguş-Lasnier, Benguş-Lasnier, Andrei, Antoni Rangachev +1
Engineering · Mathematics · #13C40 #13H15 #14B07 #14C17 #14H20 #14H50 #14M06 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2504.09362

openalex publication_date 2025/04/12 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

Abstract

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.

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