Abstract

Given an embedding of a smooth projective curve X of genus g≥1 into PN, we study the locus of linear subspaces of PN of codimension 2 such that projection from said subspace, composed with the embedding, gives a Galois morphism X→P1. For genus g≥2 we prove that this locus is a smooth projective variety with components isomorphic to projective spaces. If g=1 and the embedding is given by a complete linear system, we prove that this locus is also a smooth projective variety whose positive-dimensional components are isomorphic to projective bundles over étale quotients of the elliptic curve, and we describe these components explicitly.