The Noether exponent and Jacobi formula

Abstract

For any polynomial mapping $F=(F_1,\dots ,F_n)$ of $\Cal C^n$ with a finite number of zeros we define the Noether exponent $ν(F)$. We prove the Jacobi formula for all polynomials of degree strictly less than $\sum_{i=1}^n (°F_i-1)-ν(F)$.