Jacobian Conjecture in two dimension

2013/06/14 by Joe, Dosang
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 14R15 #Secondary: 37D15

paper · doi:10.48550/arxiv.1306.3314

Abstract

Let (P, Q) be a pair of Jacobian polynomials. We can show that +l+2g(P)-2= 0= , where is the intersection number of f, g∈ \CC[x, y] in the affine plane, l is the number of branch at point at infinity and g(P) is the geometric genus of affine curve defined by P. Hence we can show that every Jacobian polynomial defines a smooth rational curve with one point at infinity. It is sufficient to fix the Jacobian conjecture in two dimension by the Abhyankar theorem or the Abhyankar-Moh-Suzuki theorem.

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