English

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.

Keywords

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

R2 v1 2026-06-24T02:59:36.465Z