Severi's theorem for d-uple Veronese varieties

TL;DR

This paper characterizes d-uple Veronese embeddings of finite-dimensional projective spaces, extending classical results like Severi's theorem for complex projective planes to more general settings.

Contribution

It provides a comprehensive characterization of d-uple Veronese embeddings, generalizing Severi's classical theorem beyond complex fields.

Findings

Characterization of d-uple Veronese embeddings

Extension of Severi's theorem to broader contexts

Identification of key properties of these embeddings

Abstract

We characterize $d$-uple Veronese embeddings of finite-dimensional projective spaces. The easiest non-trivial instance of our theorem is the embedding of the projective plane in 5-dimensional projective space, a result obtained in 1901 by Severi when the underlying field is complex.