Commutative algebraic monoid structures on affine surfaces

TL;DR

This paper classifies commutative algebraic monoid structures on normal affine surfaces, providing a comprehensive understanding of their algebraic and geometric properties in characteristic zero.

Contribution

It offers a complete classification of such monoid structures using comultiplications and Cox coordinates, extending to higher-dimensional cases.

Findings

Classification of monoid structures on affine surfaces

Use of Cox coordinates for description

Extension to higher-dimensional varieties

Abstract

We classify commutative algebraic monoid structures on normal affine surfaces over an algebraically closed field of characteristic zero. The answer is given in two languages: comultiplications and Cox coordinates. The result follows from a more general classification of commutative monoid structures of rank 0, n-1 or n on a normal affine variety of dimension n.