All Questions
Tagged with quivers quiver-varieties
9
questions
34
votes
3
answers
1k
views
How is the free modular lattice on 3 generators related to 8-dimensional space?
Here are three facts which sound potentially related. What are the actual relationships?
In 1900, Dedekind constructed the free modular lattice on 3 generators as a sublattice of the lattice of ...
- 21k
6
votes
1
answer
540
views
For which quiver varieties is Kirwan surjectivity known?
The cohomology of Nakajima quiver varieties is a quite interesting object. It's equipped with some natural classes given by the Chern classes of the tautological bundles associated to the spaces in ...
- 43.4k
5
votes
0
answers
254
views
Intuition for the McGerty-Nevins compactification of quiver varieties
In Section 4 of the paper Kirwan surjectivity for quiver varieties (Inventiones Math. 2018) McGerty and Nevins define a compactification of the moduli space of representations
of the preprojective ...
- 2,481
3
votes
0
answers
97
views
Example of an irreducible component with an open set of infinitely many codimension 2 (codimension 3) orbits
Let $\mathbb{K}$ be an algebraically closed field of characteristics $0$. Let $A$ be a finite dimensional (associative and unital) algebra over $\mathbb{K}$. Assume there is a quiver $Q=(Q_0,Q_1)$, ...
- 757
2
votes
0
answers
113
views
Two notions of stability
Let $Q$ be a finite quiver (i.e. an oriented graph). A representation of $Q$ is by definition a module over the path algebra of $Q$. More concretely, a representation associates to every vertex $v \in ...
- 373
2
votes
0
answers
109
views
Getting an equivariant morphism
Let $X\subset\mathbb{A}^n$ be an irreducible affine variety over an algebraically closed field $\mathbb{K}$ of characteristic zero. Suppose we have two linearly reductive algebraic groups $G$, $G'$ ...
- 757
1
vote
0
answers
122
views
How to determine if an invariant rational function is defined at the $\theta$-polystable point
Background:
Let $A$ be a finite-dimensional (associative and unital) algebra over $\mathbb{C}$. Assume there is a quiver $Q=(Q_0,Q_1)$, where $Q_0$ is the set of vertices and $Q_1$ is the set of ...
- 757
1
vote
0
answers
95
views
Is $U\subseteq X^{s}(L)$?
Let $X$ be an irreducible affine variety over an algebraically closed field $\mathbb{K}$ of characteristics $0$. Let $G$ be a connected, linearly reductive, affine algebraic group acting regularly on $...
- 757
1
vote
0
answers
131
views
Non-empty stable locus of an irreducible component
I have a vague question:
Let $X$ be an algebraic pre-scheme and $G$ be a linear reductive group. Consider the G.I.T. quotient $X{/\!/}G$. Is there any result (maybe in some special case) which tells ...
- 757