Topology and Factorization of Polynomials

Details Topology and Factorization of Polynomials Topology and Factorization of Polynomials

2007-04-25

arxiv.org/abs/0704.3363v2

Mathematics

Algebraic Geometry

Accepted in Mathematica Scandinavica. 8 pages

Scientific paper

For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$ is the number of irreducible factors of $P$. Moreover, the knowledge of $F(P)$ gives a complete factorization of the polynomial $P$ by taking gcd's. This generalizes previous results by Ruppert and Gao in the case $n=2$.

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