On the multiplicity of solutions of a system of algebraic equations

2012/05/09 by Pukhlikov, Aleksandr
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1205.1995

Abstract

We obtain upper bounds for the multiplicity of an isolated solution of a system of equations f₁=...= f_M =0 in M variables, where the set of polynomials (f₁,..., f_M) is a tuple of general position in a subvariety of a given codimension which does not exceed M, in the space of tuples of polynomials. It is proved that for M→∞ that multiplicity grows not faster than √(M)exp[ω√(M)], where ω>0 is a certain constant.

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