Topology and factorization of polynomials - Shaker, Hani (MATHEMATICA SCANDINAVICA, 2009)
For any polynomial PC [X_1,X_2,…,X_n], we describe a 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.