All Questions
12 questions
22
votes
2
answers
2k
views
A royal road to Coulomb branches of 3D $\mathcal{N}=4$ gauge theories
So, I've been very interested recently with the developements of the (now mathematically precise) theory of Coulomb branches - in particular because of its recent applications on representation theory ...
- 3,318
14
votes
2
answers
1k
views
Information from Moment Polytopes
Let $T$ be a compact real torus, and $X$ a Hamiltonian $T$-manifold (which you may take to be a smooth complex projective variety) with moment map $\mu:X\rightarrow\frak{t}^*$. If $\dim(T)=\frac{1}{2}\...
- 4,920
11
votes
2
answers
2k
views
Classification of symplectic resolutions
A. Okounkov said, "symplectic resolutions are Lie algebras of the 21st century." Is there a conjecture on the classification of symplectic resolutions? Do Braverman-Finkelberg-Nakajima Coulomb ...
- 2,964
7
votes
1
answer
710
views
Bialynicki-Birula Decomposition and moment polytopes/graphs
Let $X$ be a possibly singular projective scheme which admits a torus $T$ action and has finitely many $T$ fixed points and one-dimensional $T-$orbits. There are many such schemes in the Grassmannian/...
- 1,719
6
votes
4
answers
716
views
Prequantization and Hilbert space
In the definition of pre-quantization on a symplectic manifold $(M,\omega)$, we represent a function $f\in C^{\infty}(M)$(with Lie algebra structure) to $\hat{f}$ in the Hilbert space $L^2(M,L,\mu)$ ...
user21574
6
votes
1
answer
139
views
Quiver variety, generically symplectic
Theorem 11.3.1 (iv) of "Noncommutative Geometry and Quiver algebras" by Crawley-Boevey, Etingof and Ginzburg claims that, for a dimension vector $\mathbf{d}\in\Sigma_0$, the quiver variety $...
- 985
6
votes
1
answer
465
views
Splitting principle in equivariant cohomology
The following is a weaker version of what is called splitting principle in
Appendix C, page 12, see also for a lighter version Brions Eq cohom and eq intersection theory, page 6:
Let $G$ be a compact ...
- 103
5
votes
1
answer
408
views
Descent of vector bundle along branched cover of curve
Suppose $\pi:C'\to C$ is a branched cover of compact Riemann surfaces such that the associated extension of function fields is Galois with group $G$ -- so that $\pi$ presents $C$ as the quotient $C'$ ...
- 1,761
4
votes
0
answers
189
views
Fibers of torus equivariant moment maps
Given a closed (possibly singular) projective variety $V$ with a symplectic structure and a torus action, there is a moment map
$\mu: V \rightarrow Lie(T)^*$. Note that the dimension of $T$ could be ...
- 1,719
3
votes
0
answers
150
views
Integral Homology of GIT Quotients
Is there any example of GIT quotients of linear actions on a Euclidean space ${\mathbb C}^n$ that satisfy the following conditions?
The quotient is compact and smooth.
The homology of the quotient ...
- 1,207
2
votes
2
answers
2k
views
Semistability in GIT
If I understand correctly, in geometric invariant theory, polystable points can be defined as those which have a closed orbit. Is it true that semistable points can be characterized as those whose ...
- 1,347
2
votes
1
answer
306
views
connectedness of fibers of torus-equivariant moment maps
Given a possibly singular, connected, symplectic algebraic variety with a torus action, every fiber of the moment map admits a torus action. Is each fiber of this moment map connected? Any examples or ...
- 1,719