# Tagged Questions

**6**

votes

**1**answer

544 views

### Are there workable algebraic geometry approaches for the pentagon equation?

A pentagon equation is a system of polynomial equations of degree $3$ with several variables and integer coefficients, given by a fusion ring.
A fusion ring is given by a finite set of integer ...

**1**

vote

**1**answer

206 views

### smooth quotient out of a singular variety?

If $X$ is a smooth quasi-projective variety over $\mathbb{C}$ and $G$ is a finite group acting faithfully on $X$, then the Shepard-Todd theorem gives us some criterion for $X/G$ to be smooth.
My ...

**2**

votes

**2**answers

302 views

### Finite Quotients and Resolutions of Singularities

So, I feel like I'm missing something obvious, but I have the following situation:
Let $X\to Y$ be a finite group quotient of schemes (in fact, varieties) by the finite group $G$. Let $\tilde{Y}\to ...

**3**

votes

**2**answers

302 views

### Quotient of a rational variety by a finite group

Let $X$ be a rational variety and let $G$ be a finite group acting on $X$. Let us consider the diagonal action of $G$ over the product $X^{h} = X\times...\times X$,
$$G\times(X\times...\times ...

**3**

votes

**1**answer

272 views

### quotient by finite group actions that are smooth

Let $X$ an affine normal scheme of finite type over a field $k$ of characteristic zero.
Let $G$ a finite group acting on $X$ and $Y=X/G=Spec(K[X]^{G})$.
We assume that ...

**2**

votes

**1**answer

125 views

### Embeddings of of quotient singularities

Let $G$ be a finite subgroup of $SL(n,\mathbb{C})$. Let $G$ act on $\mathbb{C}^{n}$ with the action induced by $SL(n,\mathbb{C})$ and the induced action of $G$ on the unit sphere $S^{2n-1}$ is free. ...

**10**

votes

**2**answers

435 views

### Finite subgroups of $PGL(3,K)$

It is well-known that finite subgroups of $PGL_2(\mathbb{C})$ are cyclic groups, dihedral groups, A4, S4 and A5 and each of these groups occurs exactly once (up to conjugacy). These facts are ...

**0**

votes

**0**answers

78 views

### Building an invariant Sn structure from two invariant Zn structures

Take two mathematical structures with a $Z_n$ symmetry (cyclic symmetry). Which are the different ways, in "gluing" these structures, to obtain a mathematical structure with a $S_n$ symmetry ...

**1**

vote

**2**answers

223 views

### Is the zero set of a equivariant polynomial map of minimal degree a union of linear subspaces?

Suppose that a finite group acts on two vector spaces $X$ and $Y$, and that $f:X\longrightarrow Y$ is an equivariant polynomial map which is homogeneous of degree $n$, and that there does not exist ...

**6**

votes

**2**answers

484 views

### Spherical building of an exceptional group of Lie type

I've read that one of Tits' original motivations for studying buildings was that he wanted to give a unified description of algebraic groups that would allow the definition of exceptional groups such ...

**4**

votes

**1**answer

273 views

### finite quotients of fundamental groups in positive characteristic

For affine smooth curves over $k=\bar{k}$ of char. $p,$ Abhyankar's conjecture (proved by Raynaud and Harbater) tells us exactly which finite groups can be realized as quotients of their fundamental ...

**24**

votes

**1**answer

895 views

### How does one compute invariants of certain Grassmannians inside the regular representation?

Barry Mazur and I have come across the question below, motivated by (but independent
of) issues regarding the Leopoldt conjecture.
Suppose that $\mathbf{C}$ is the complex numbers.
Let $H$ be a ...

**7**

votes

**1**answer

408 views

### Extending group actions on varieties

Let $X$ be a (irreducible) variety (over $\mathbb{C}$ if necessary, smooth orbifold if necessary), and $U\subset X$ a nonempty open subset, and let $G$ be a finite group with an algebraic action on ...

**4**

votes

**2**answers

352 views

### Finite group scheme acting on a scheme such that there is an orbit NOT contained in an open affine.

In Mumfords book on abelian varieties there is a theorem (on page 111) whose hypothesis is "Let G be a finite group scheme acting on a scheme X such that the orbit of any point is contained in an ...

**13**

votes

**0**answers

512 views

### How much has been written down about Deligne's geometric approach to the order formula for a finite group of Lie type?

This is a follow-up to a recent mathoverflow question
34387
about computing the orders of finite unitary groups and the comments made there.
Between 1955 (Chevalley's Tohoku paper) and 1968 ...