The geometric-invariant-theor tag has no wiki summary.

**11**

votes

**1**answer

1k views

### When is fiber dimension upper semi-continuous?

Suppose f:*X*→Y is a morphism of schemes. We can define a function on the underlying topological space Y by sending y∈Y to the dimension of the fiber of f over y. When is this function upper ...

**4**

votes

**2**answers

223 views

### Understanding the definition of the quotient stack $[X/G]$

I'm trying to understand the definition of the quotient stack $[X/G]$ as defined in Frank Neumann's Algebraic Stacks and Moduli of Vector Bundles.
Explicitly, let $G$ be an affine smooth group ...

**2**

votes

**2**answers

217 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 ...