On rational normal curves in projective space
E. Carlini, M. V. Catalisano

TL;DR
This paper investigates the existence of rational normal curves intersecting given linear spaces in projective space, introduces methods for proving existence or non-existence, and applies these to study defectivity in Segre-Veronese varieties.
Contribution
It generalizes Veronese's classical result by developing new techniques to analyze rational normal curves in complex configurations and their applications to algebraic geometry.
Findings
Methods for proving existence of rational normal curves
Criteria for non-existence of such curves
Applications to defectivity of Segre-Veronese varieties
Abstract
In this paper we consider a generalization of a well known result by Veronese about rational normal curves. More precisely, given a collection of linear spaces in we study the existence of rational normal curves intersecting each component of the configuration maximally. We introduce different methods to show existence and non-existence of such curves. We also show how to apply these techniques to the study of defectivity of Segre-Veronese varieties.
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