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arXiv · 1809.05291

Commutative algebraic monoid structures on affine spaces

Ivan Arzhantsev·Sergey Bragin·Yulia Zaitseva
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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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Ivan Arzhantsev, Sergey Bragin, Yulia Zaitseva. 2018-09-14. Commutative algebraic monoid structures on affine spaces. https://doi.org/10.1142/s0219199719500640

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