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Preprints, Working Papers, ... Year : 2014

On curves with one place at infinity

Pedro A. García-Sánchez
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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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Dates and versions

hal-01016473 , version 1 (02-07-2014)


  • HAL Id : hal-01016473 , version 1


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