All Questions
Tagged with toric-varieties rt.representation-theory
10
questions
2
votes
0
answers
127
views
Abstract definition of hypertoric varieties
I'm reading Proudfoot's survey on hypertoric varieties. In Section 1.4 he mentioned such a conjecture:
Conjecture 1.4.2 Any connected, symplectic, algebraic variety which is projective over its ...
- 271
2
votes
0
answers
147
views
Line bundles on toric varieties associated to Weyl chamber
I am interested in studying toric varieties associated to the fan of Weyl chambers. General information would be best but I am also interested in the specific case of the Weyl chamber of $\mathfrak{sl}...
- 41
3
votes
0
answers
93
views
Structure of fibers of (complex) moment map of hypertoric variety
I am primarily interested in the hypertoric variety $\mathfrak M(\mathcal B_d)$ associated to the braid arrangement.
Any hypertoric variety $X$, say of complex dimension $2n$, comes equipped with an ...
- 71
5
votes
0
answers
116
views
Where to read about the toric variety coming from a principal nilpotent element of a (semi)simple algebraic group?
Given a principal (regular) nilpotent element $e$ in the Lie algebra $\mathfrak g$ of a complex semisimple algebraic group $G$, let $\mathfrak s=(e,f,h)$ be an $\mathfrak{sl}_2$-triple for $e$. Then ...
- 17.8k
4
votes
0
answers
214
views
Local structure of non-normal toric varieties---possible mistake in "Discriminants, Resultants and Multidimensional Determinants"
I believe I may have a counterexample to Theorem 5.3.1 on page 179 from the book book Discriminants, Resultants and Multidimensional Determinants by Gel'fand, Kapranov, and Zelevinsky. To summarize ...
- 3,039
6
votes
2
answers
299
views
Irreducibility of Gelfand-Serganova strata
To keep the notations simple I'll restrict my attention to the complete flag variety although the question should be equally valid for partial flag varieties. Consider $G=SL_n(\mathbb C)$ with Borel $...
- 3,503
9
votes
1
answer
926
views
Closures of torus orbits in flag varieties
Consider the Lie group $G=SL_n(\mathbb C)$ with Borel subgroup $B$ and maximal torus $T\subset B$. I'm interested in the (Zariski) closures of $T$-orbits in the flag variety $F=G/B$.
Now, as far as I ...
- 3,503
4
votes
1
answer
192
views
Number of boundary divisors and colors of a Spherical variety
Let $X$ be a Spherical variety for a reductive group $G$ with a Borel subgroup $B$. A boundary divisor of $X$ is a $G$-invariant divisor and a color of $X$ is a $B$-invariant divisor which is no $G$-...
user75933
1
vote
0
answers
222
views
Equivariant derived category versus graded derived category
Everything here has the Zariski topology.
Let $T=(\Bbb{C}^*)^d$, and define an action of $T$ on $\Bbb{C}^n$ by $$t\cdot x=(t^{\mathbf{a}_1}x_1,\ldots, t^{\mathbf{a}_n}x_n).$$ Here $\mathbf{a}_1,\...
- 3,039
12
votes
2
answers
1k
views
Is an affine "G-variety" with reductive stabilizers a toric variety?
Let $X=Spec(A)$ be a reduced normal affine scheme over an algebraically closed field $k$ of characteristic $0$, with an action of a connected reductive group $G$. Suppose
$x\in X$ is a $G$-...
- 23.8k