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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

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.