Approximate roots, toric resolutions and deformations of a plane branch

作者：Gonzalez Perez Pedro Daniel

来源：Journal of the Mathematical Society of Japan, 2010, 62(3): 975-1004.

DOI：10.2969/jmsj/06230975

• approximate roots
• deformations of a plane curve
• equisingularity criterion

We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of C{x}[y], defining a plane branch (C, 0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C, 0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch.

• 出版日期2010-7