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Commutative algebraic monoid structures on affine spaces

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arxiv 1809.05291 v2 pith:FAH7HJ43 submitted 2018-09-14 math.AG

Ivan Arzhantsev , Sergey Bragin , Yulia Zaitseva This is my paper · ORCID
classification math.AG
keywords mathbbaffinecommutativeoperationsalgebraicdimensionspacesactions
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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.

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  1. Additive actions on complete toric surfaces

    math.AG 2019-08 conditional novelty 6.0 of 10

    A complete toric surface admitting an additive action has exactly one such action if its fan is wide, and two non-isomorphic actions otherwise.

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