2024/08/28 by Carlos Galindo, Galindo, C., Francisco Monserrat +5
Mathematics · Engineering · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Advanced Numerical Analysis Techniques
paper · pdf · doi:10.48550/arxiv.2408.15931
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.