Interpolation of Varieties of Minimal Degree

TL;DR

This paper generalizes the classical result about rational normal curves passing through points to higher-dimensional varieties, demonstrating that smooth minimal degree varieties can be uniquely interpolated through points and linear spaces.

Contribution

It extends the interpolation property from rational normal curves to higher-dimensional smooth varieties of minimal degree.

Findings

Smooth minimal degree varieties can be interpolated through points and linear spaces.

The classical interpolation result for rational normal curves is generalized to higher dimensions.

The paper establishes conditions for interpolation of these varieties.

Abstract

It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated through points and linear spaces.