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arXiv · 2205.04184

On linear systems with multiple points on a rational normal curve

Antonio Laface·Elisa Postinghel·Luis José Santana Sánchez
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Abstract

We give a closed formula for the dimension of all linear systems in $\mathbb{P}^n$ with assigned multiplicity at arbitrary collections of points lying on a rational normal curve of degree $n$. In particular we give a purely geometric explanation of the speciality of these linear systems, which is due to the presence of certain subvarieties in the base locus: linear spans of points, secant varieties of the rational normal curve or joins between them.

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Antonio Laface, Elisa Postinghel, Luis José Santana Sánchez. 2022-05-09. On linear systems with multiple points on a rational normal curve. https://arxiv.org/abs/2205.04184

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