Quotients by non-reductive algebraic group actions

TL;DR

This paper explores how to construct quotients of complex projective varieties by non-reductive algebraic groups, focusing on reductive envelopes and applications to moduli spaces of hypersurfaces in weighted projective planes.

Contribution

It introduces methods for forming reductive envelopes for non-reductive group actions and applies these to specific moduli space examples.

Findings

Constructed reductive envelopes for non-reductive group actions.

Analyzed moduli spaces of hypersurfaces in weighted projective planes.

Provided examples illustrating the theory's application.

Abstract

Given a suitable action on a complex projective variety X of a non-reductive affine algebraic group H, this paper considers how to choose a reductive group G containing H and a projective completion of G x_H X which is a reductive envelope in the sense of math.AG/0703131. In particular it studies the family of examples given by moduli spaces of hypersurfaces in the weighted projective plane P(1,1,2) obtained as quotients by linear actions of the (non-reductive) automorphism group of P(1,1,2).