The bifurcation set of a real polynomial function of two variables and Newton polygons of singularities at infinity

2016/08/09 by Ishikawa, Masaharu, Nguyen, Tat Thang, Pham, Tien Son
#32S30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Primary: 32S20 #Secondary: 32S15

paper · doi:10.48550/arxiv.1608.02679

Abstract

In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactification. We also count the number of singular phenomena at infinity, called "cleaving" and "vanishing" in the same setting. Finally, we give an upper bound of the number of elements in the bifurcation set in terms of its Newton polygon. To obtain the upper bound, we apply toric modifications to the singularities at infinity successively.

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