On rational normal curves in projective space

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 $\PP^n$ 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.