The image of the Veronese mapping is a determinantal variety; an elementary proof

Author:

Rahim Zaare-Nahandi

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-09-20 16:00:00

Abstract

Let $\nu_d : \mathbb{P}^n \longrightarrow \mathbb{P}^N$ be the Veronese mapping of degree $d$ where $N = {n+d \choose n} -1$. By an elementary approach it is shown that $\nu_d$ is an isomorphism of $\mathbb{P}^n$ onto the projective variety defined by the $2$-minors of a matrix.

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