Embeddings of C*-surfaces into weighted projective spaces

TL;DR

This paper demonstrates that many normal affine surfaces with specific group actions can be embedded into weighted projective spaces, extending known results and providing new embedding techniques.

Contribution

It introduces a method to embed C*- and C+-action surfaces into weighted projective hypersurfaces, generalizing previous results by Daigle and Russell.

Findings

Many C*- and C+-action surfaces can be embedded into weighted projective hypersurfaces.

The approach recovers and extends previous embedding results.

Provides a framework for understanding embeddings of affine surfaces with group actions.

Abstract

Let V be a normal affine surface which admits a C*- and a C+-action. In this note we show that in many cases V can be embedded as a principal Zariski open subset into a hypersurface of a weighted projective space. In particular, we recover a result of D. Daigle and P. Russell.