On curves with one place at infinity

2014/07/02 by Abdallah Assi, Assi, Abdallah, Pedro A. García-Sánchez +1
Computer Science · Mathematics · #14Q05 #14R05 #20M14 #68W01 #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1407.0490

openalex publication_date 2014/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a plane curve. We give a procedure based on Abhyankar's approximate roots to detect if it has a single place at infinity, and if so construct its associated δ-sequence, and consequently its value semigroup. Also for fixed genus (equivalently Frobenius number) we construct all δ-sequences generating numerical semigroups with this given genus. For a δ-sequence we present a procedure to construct all curves having this associated sequence. We also study the embeddings of such curves in the plane. In particular, we prove that polynomial curves might not have a unique embedding.

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