Intersection multiplicity, Milnor number and Bernstein's theorem

Pinaki Mondal

Published 2016-07-17Version 1

We compute the intersection multiplicity at the origin of n generic polynomials (over an algebraically closed field K) with fixed Newton diagrams and present a Bernstein-Kushnirenko type characterization of what it means to be 'generic'. This leads to the 'correct' formulation of non-degeneracy of a polynomial with respect to its Milnor number. As another application we compute the number of isolated solutions (counted with multiplicity) in K^n of n generic polynomials with fixed Newton polytopes, with an explicit characterization of non-degeneracy.