2024/08/02 by Lee, Kyungyong, Li, Li
#11P21 #14M25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 14R15 Secondary: 13F20
paper · doi:10.48550/arxiv.2408.01279
Let (F,G) be a Jacobian pair with d=w-deg(F) and e=w-deg(G) for some direction w. A generalized Magnus' formula approximates G as ∑γ≥ 0 cγF(e-γ)/(d) for some complex numbers cγ. We develop an approach to the two-dimensional Jacobian conjecture, aiming to minimize the use of terms corresponding to γ>0. As an initial step in this approach, we define and study the inner polynomials of F and G. The main result of this paper shows that the northeastern vertex of the Newton polygon of each inner polynomial is located within a specific region. As applications of this result, we introduce several conjectures and prove some of them for special cases.