# 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.
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https://hal.archives-ouvertes.fr/hal-01016473
Contributor : Abdallah Assi <>
Submitted on : Wednesday, July 2, 2014 - 8:41:45 AM
Last modification on : Monday, March 9, 2020 - 6:15:54 PM
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Semigroup_of_Values.pdf
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• HAL Id : hal-01016473, version 1

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

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