English

Genus one factors of curves defined by separated variable polynomials

Number Theory 2014-09-09 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1409.2216,
  title  = {Genus one factors of curves defined by separated variable polynomials},
  author = {Ta Thi Hoai An and Nguyen Thi Ngoc Diep},
  journal= {arXiv preprint arXiv:1409.2216},
  year   = {2014}
}
R2 v1 2026-06-22T05:50:53.280Z