# On curves with one place at infinity

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 $\delta$-sequence, and consequently its value semigroup. Also for fixed genus (equivalently Frobenius number) we construct all $\delta$-sequences generating numerical semigroups with this given genus. For a $\delta$-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.
Keywords :
Type de document :
Pré-publication, Document de travail
2014

Littérature citée [12 références]

https://hal.archives-ouvertes.fr/hal-01016473
Contributeur : Abdallah Assi <>
Soumis le : mercredi 2 juillet 2014 - 08:41:45
Dernière modification le : lundi 5 février 2018 - 15:00:03
Document(s) archivé(s) le : jeudi 2 octobre 2014 - 10:37:04

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Semigroup_of_Values.pdf
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• HAL Id : hal-01016473, version 1

### Citation

Abdallah Assi, Pedro A. García-Sánchez. On curves with one place at infinity. 2014. 〈hal-01016473〉

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