On toric ind-varieties and pro-affine semigroups

Affine Cones over Algebraic Varieties and Embeddings into Toric Prevarieties

Cox Rings, Semigroups and Automorphisms of Affine Algebraic Varieties

We study the Cox realization of an affine variety, i.e., a canonical representation of a normal affine variety with finitely generated divisor class group as a quotient of a factorially graded affine variety by an action of the Neron-Severi quasitorus. The realization is described explicitly for the quotient space of a linear action of a finite group. A universal property of this realization is...

Minicourse on Toric Varieties

1. Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Characters and 1-Parameter Subgroups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3. Toric Varieties . . . . . . . . . . . . . . . . . . . . . . . . . ....

Lectures on Toric Varieties

1 Four constructions 1 1.1 First construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Second construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Third construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourth construction . . . . . . . . . . . . . . . . . . . . . . . . . . ...

Comments on toric varieties

Here are few notes on not necessarily normal toric varieties and resolution by toric blow-up. These notes are independent of, but in the same spirit as the earlier preprint [Tho03]. That is, they focus on the fact that toric varieties are locally given by monoid algebras. 1 Not necessarily normal toric varieties Fix a base field k. We start by recalling the definition of a fan. Let N ∼= Z be a ...