Семинар НУЛ АГП "Algebraic monoids with affine group of invertible elements"

Let X be an algebraic variety with a monoid structure, i.e., there is an associative multiplication X × X → X, which is a morphism of algebraic varieties and admits a neutral element. Denote the group of invertible elements by G(X). It is known that G(X) is an algebraic group, open in X. It is easy to see that if X is affine, then G(X) is affine as well. We plan to prove the converse: if G(X) is an affine algebraic group, then the variety X is also affine. The talk is based on [1].

[1] Alvaro Rittatore. Algebraic monoids with affine unit group are affine. Transform. Groups 12 (2007), no. 3, 601-605