Commutative algebraic monoid structures on affine spaces

Abstract

We study commutative associative polynomial operations ${\mathbb{A}}^n\times {\mathbb{A}}^n\to {\mathbb{A}}^n$ with unit on the affine space ${\mathbb{A}}^n$ over an algebraically closed field of characteristic zero. A classification of such operations is obtained up to dimension 3. Several series of operations are constructed in arbitrary dimension. Also we explore a connection between commutative algebraic monoids on affine spaces and additive actions on toric varieties.

arXiv comment19 pages

References in corpus (1)

• Additive actions on toric varieties

Cited by in corpus (6)

• Commutative algebraic monoid structures on affine surfaces
• Root subgroups on affine spherical varieties
• Affine monoids of corank one
• Algebraic monoid structures on the affine 3-space
• On conjugacy of additive actions in the affine Cremona group
• Equivariant completions of affine spaces