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On Abhyankar's irreducibility criterion for quasi-ordinary polynomials

2018/04/15 by Janusz Gwoździewicz, Gwoździewicz, Janusz, Beata Hejmej +1
Mathematics · #14H20 #32S55 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1804.05366

openalex publication_date 2018/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f 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 degree of g is small enough and all monomials appearing in the resultant of f and g have orders big enough, then g is irreducible and quasi-ordinary, generalizing Abhyankar's irreducibility criterion for plane analytic curves.

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