Galois subspaces for the rational normal curve

TL;DR

This paper classifies all linear subspaces of projective space that induce Galois morphisms on the rational normal curve, providing an explicit geometric description within the Grassmannian.

Contribution

It characterizes all (n-2)-dimensional subspaces leading to Galois projections on the rational normal curve and describes their structure in the Grassmannian.

Findings

Explicit description of Galois subspaces as disjoint unions in the Grassmannian.

Complete classification of linear projections inducing Galois morphisms.

Structural insight into the geometry of these subspaces.

Abstract

We characterize all $(n-2)$-dimensional linear subspaces of $\mathbb{P}^{n}$ such that the induced linear projection, when restricted to the rational normal curve, gives a Galois morphism. We give an explicit description of these spaces as a disjoint union of locally closed subvarieties in the Grassmannian $\mathbb{G}(n-2,n)$.