Veronese Varieties over Fields with non-zero Characteristic: A Survey

TL;DR

This survey reviews recent findings on the nuclei of Veronese varieties and invariant subspaces of rational curves, emphasizing the importance of the field's size in these geometric structures.

Contribution

It compiles recent results on Veronese varieties over fields with non-zero characteristic, highlighting conditions for their geometric properties.

Findings

Nuclei of Veronese varieties are characterized under certain field conditions.

Invariant subspaces of normal rational curves are analyzed.

Field size influences the geometric complexity of these varieties.

Abstract

In the present survey we collect some recent results on nuclei of Veronese varieties and invariant subspaces of normal rational curves. We must assume, however, that the ground field is not "too small", since otherwise a Veronese variety is like dust: "few points" in some "high-dimensional" space.