On the Abhyankar–Moh irreducibility criterion for quasi-ordinary polynomials
Tom 164 / 2021
Colloquium Mathematicum 164 (2021), 149-160
MSC: Primary 32S55; Secondary 14H20.
DOI: 10.4064/cm8116-2-2020
Opublikowany online: 18 September 2020
Streszczenie
Let and g be Weierstrass polynomials with coefficients in the ring of formal power series over an algebraically closed field of characteristic zero. Assume that f is irreducible and quasi-ordinary. We show that if the degree of g is small enough and all monomials appearing in the resultant of f and g have orders large enough, then g is irreducible and quasi-ordinary. This generalizes the Abhyankar–Moh irreducibility criterion for plane analytic curves.
