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arXiv · 2408.15931

On $δ$-sequences and surfaces at infinity

C. Galindo·F. Monserrat·C. -J. Moreno-Ávila·J. -J. Moyano-Fernández
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Abstract

In most cases the semigroup at infinity $S$ of a curve $C$ with only one place at infinity is generated by a $δ$-sequence. This sequence provides geometrical information on $C$ such as the dual graph of the resolution of the singularity of $C$ at infinity. Since different $δ$-sequences can generate the same semigroup, it is an interesting problem to know the geometrical behaviour of curves $C$ sharing the same semigroup $S$. An analogous problem arises in a more general context when considering surfaces at infinity and their $δ$-semigroups. We show how to construct $δ$-sequences, and how to obtain different families that generate the same semigroup $S$, allowing us to study the geometrical content encoded by $S$.

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C. Galindo, F. Monserrat, C. -J. Moreno-Ávila, J. -J. Moyano-Fernández. 2026-04-08. On $δ$-sequences and surfaces at infinity. https://arxiv.org/abs/2408.15931

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