Classification of noncommutative monoid structures on normal affine surfaces
Algebraic Geometry
2021-07-16 v2
Abstract
In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional algebraic monoids are toric. We also show how to find all monoid structures on a normal toric surface. Every such structure is induced by a comultiplication formula involving Demazure roots. We also give descriptions of opposite monoids, quotient monoids, and boundary divisors.
Cite
@article{arxiv.2106.04884,
title = {Classification of noncommutative monoid structures on normal affine surfaces},
author = {Boris Bilich},
journal= {arXiv preprint arXiv:2106.04884},
year = {2021}
}
Comments
14 pages, minor corrections