1
vote
0answers
47 views

on reductive monoids which are gorenstein

Let $M$ a reductive monoid, i.e. a integral normal affine scheme, which is a monoid whose group of units is a connected reductive group. By Rittatore ...
3
votes
0answers
122 views

What is the combinatorial data classifying non-normal affine toric varieties?

Recall that a toric variety is a variety $V$ containing an open dense algebraic torus. Here an algebraic torus means a finite product of copies of the multiplicative group of the ground field (which I ...
1
vote
2answers
226 views

Are orbits of an affine algebraic monoid affine?

Let us work over the complex numbers for simplicity. Let $M$ be an affine algebraic monoid and $X$ an affine variety on which $M$ acts regularly, i.e. there is a morphism $\alpha: M\times X\to X$. Let ...
3
votes
0answers
138 views

determine if a toric variety is Gorenstein

Let $G$ a simply connected group over $k$ and $car(k)=0$. Let $T_{+}=(T\times T)/Z_{G}$ we consider the closure $\overline{T}_{+}$ of the torus $T_{+}$ in $\prod ...
4
votes
0answers
214 views

What is the pro-algebraic completion of the free semigroup on one generator?

This question is motivated by an attempt to understand what is going on in Tom's post from a certain point of view. Let $\mathbb N^+$ be the free semigroup on one generator (so the positive natural ...
7
votes
1answer
389 views

Cones, monoids, and the space of (very) ample divisors

An interesting and useful tool to study a projective variety is its ample cone. Understanding the structure of this cone reveals information about the variety, and it is an isomorphism-invariant so ...