On linear systems with multiple points on a rational normal curve

2022/05/09 by Laface, Antonio, Postinghel, Elisa, Sánchez, Luis José Santana · 1 citation
#14C20 #14J17 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.04184

Abstract

We give a closed formula for the dimension of all linear systems in ℙⁿ 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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• On defectivity of joins, reducible secants and Fröberg's conjecture

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