Automorphisms and the canonical ideal

TL;DR

This paper investigates the automorphism group of algebraic curves through their canonical embeddings, providing criteria for their algebraic subgroup structure and extending the automorphism action to the canonical ring's minimal free resolution.

Contribution

It introduces a new criterion for identifying automorphism groups as algebraic subgroups of the general linear group and extends their action to the canonical ring's minimal free resolution.

Findings

Automorphism groups can be characterized as algebraic subgroups of GL(n).

The action of automorphisms extends to the minimal free resolution of the canonical ring.

New criteria link automorphism groups to canonical embeddings and Petri's theorem.

Abstract

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the action of the automorphism group is extended to an action of the minimal free resolution of the canonical ring of the curve $X$.