# Tagged Questions

**4**

votes

**1**answer

211 views

### Smooth projective toric varieties which are quotients of product of spheres and torii by a free torus action?

My question is just as in the box. Is every smooth projective toric variety diffeomorphic to a quotient of $\prod_i S^{n_i} \times T^k$ (I know torus is a one-sphere but I just wanted to make clear I ...

**5**

votes

**2**answers

572 views

### Deformations of Hirzebruch surfaces and toric action

Hi,
the Hirzebruch surface $F_n$ admits a deformation for $0\leq m\leq n$ defined by the equation
$$
\mathcal{M}=\{ ([x_0:x_1],[y_0:y_1:y_2],t) \in \mathbb{P}^1 \times \mathbb{P}^2 \times ...

**16**

votes

**1**answer

646 views

### About a Delzant polytope. (In particular dodecahedron)

Hi. I have a question.
Definition. Delzant polytope $P$ is a rational convex simple polytope with the smooth condition. Here, "smooth" means that for each vertex $v$, the $n$ edges containing $v$ ...

**5**

votes

**0**answers

430 views

### When should a moment polytope have “smooth” faces?

A codimension $d$ face of a polytope is called rationally smooth if it lies on only $d$ facets, because this is exactly the condition for the corresponding toric variety to have only orbifold ...

**3**

votes

**2**answers

541 views

### Moment map for toric actions — online references?

Consider a toric variety, defined as a (normal?) complex projective variety $X$ together with an algebraic action of $(\mathbb C^*)^n$ with finitely many orbits. Now we have two "real symplectic" ...

**8**

votes

**2**answers

556 views

### Hamiltonian S^1 actions with isolated fixed points

I have in mind the following question for some time. Is there an example of a compact symplectic manifold with a Hamiltonian S^1 action with isolated fixed points, that does not admit a compatible S^1 ...