2013/03/28 by Ta Thi Hoai An, Diep Nguyen, Nguyen Thi Ngoc Diep · 6 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Algebraic curve #Algebraic number #Botany #Combinatorics #Component (thermodynamics) #Genus #Geometry #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Physics #Plane (geometry) #Plane curve #Pure mathematics #Variable (mathematics) #math.NT
paper · pdf · doi:10.1016/j.jnt.2012.12.017
published in Journal of Number Theory 133(8), 2616-2634 (Elsevier BV)
openalex publication_date 2013/03/28 · arxiv created 2014/09/08 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give some sufficient conditions on complex polynomials P and Q to assure that the algebraic plane curve P(x)-Q(y)=0 has no irreducible component of genus 0 or 1. Moreover, if deg (P)=deg (Q) and if both P, Q satisfy Hypothesis I introduced by H. Fujimoto, our sufficient conditions are necessary.