2015/10/14 by Vered Moskowicz, Moskowicz, Vered
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.1510.04264
16 pages
arxiv created 2016/02/03 · arxiv updated 2016/02/04
The two dimensional Jacobian Conjecture says that a morphism f:ℂ[x,y]→ ℂ[x,y] having an invertible Jacobian, is invertible. We show that a morphism f having an invertible Jacobian is invertible, in each of the following two special cases: The degree of f(x) is ≤ 2; The (0,1)-degrees or (1,0)-degrees of all monomials in f(x) are of the same parity. In each case there is no restriction on the degree of f(y) nor on the parity of the (0,1)-degrees or (1,0)-degrees of its monomials.