Jacobian Conjecture

introduction

• Let y=F(z) a polynomial system in C^n. The Jacobian Conjecture (JC) states that F is invertible, and its inverse is polynomial, if and only if the determinant of the Jacobian matrix J_F(z) = (d F_j(z)/d z_i)_{i,j=1..n} is a non-zero constant.
• what is the set of automorphisms of an affine space? Jacobian conjecture is about the polynomial automorphisms whose jacobians are constant.

• De Goursac, A., A. Sportiello, and A. Tanasa. ‘Degree Reduction in the Jacobian Conjecture, a Combinatorial Quantum Field Theoretical Approach’. arXiv:1411.6558 [hep-Th], 17 November 2014. http://arxiv.org/abs/1411.6558.

memo

• Yucai Su, Keller maps and 2-dimensional Jacobi conjecture, http://arxiv.org/abs/1603.01867v1