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Workshop on birational geometry
October 30, 2018 16:40–17:40, Moscow, Laboratory of Algebraic Geometry and its applications, Higher School of Economics

Commutative algebraic monoid structures on affine spaces

Ivan Arzhantsevab

a HSE
b MSU

Abstract: We study commutative associative polynomial operations $\mathbb{A}^n \times \mathbb{A}^n \rightarrow \mathbb{A}^n$ 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. This is a joint work with Sergey Bragin and Yulia Zaitseva.