# ag.algebraic-geometry's questions - English 1answer

14.092 ag.algebraic-geometry questions.

### 1 Plurisubharmonic function having log pole along divisor

Let $R$ be a compact Riemann surface. For a given point $p\in R$ identified to the origin $z=0$ in a coordinate chart, then the function $z$ defines a local holomorphic section vanishing along the ...

### 2 Degeneration of relative Hodge-de Rham spectral sequence


### 2 Ranks of cycles with base field coefficients as a generalization of ranks of multivectors?

This must be probably only reference request since I am inclined to believe that I am asking about something well known but just cannot pin down appropriate keywords for searching. The starting point:...

### 5 Torsion subgroup of the group of points of an elliptic curve over local field

Let $K$ be a local field with residue field $k$ and $E/K$ an elliptic curve. I'm interested for which $K$ and $E$ the group of torsion points on the curve is finite. I can prove that this group is ...

### 8 The Stacks project

I have a question concerning the admirable Stacks Project. Which comparable projects are there: approach-wise: "an open source textbook on algebraic stacks and the algebraic geometry that ...

### 3 Reference Request: Fourier Mukai on non Weierstrass Elliptic Fibration

I'm aware of the standard results about Fourier Mukai on Weierstrass elliptic fibration. What I need is the references about Fourier Mukai on elliptic fibration which can have reducible fibers and/...

### 7 What are some open problems in moduli spaces and moduli stacks?

I would like to know what are the open big and interesting problems related to moduli spaces and moduli stacks ? Thanks in advance for your help.

### 5 Algebraic independence of limit cycles of Lienard equation

It is well known that the Van der Pol equation $$\begin{cases} \dot x=y-(x^3-x)\\\dot y=-x \end{cases}$$ has no an algebraic limit cycle. According to this fact, we search for a related ...

### 7 Classification of singularities of plane curves of fixed degree (reference request)

We know the answers to some questions like What is the maximal number of singularities of (reduced) plane curves of degree $d$? for general $d$ (in this case $\tfrac{1}{2}d(d-1)$, obtained by $d$ ...

### 8 On a paper of Formanek about $PGL_4$

In his paper "The center of the ring of 4 × 4 generic matrices" (Journal of Algebra, 1980) Formanek shows that, if $V$ is the representation of $PGL_4$ given by simultaneous conjugation of pairs of ...

### 26 How to visualize Dirichlet’s unit theorem?

As the question title asks for, how do others "visualize" Dirichlet’s unit theorem? I just think of it as a result in algebraic number theory and not one in algebraic geometry. Bonus points for ...

### 2 Function is $L^p$-integrable for $p >1$ [Kähler Geometry]

I am reading through a proof in W. Ding and G. Tian's 1992 paper on the generalised Futaki invariant. To provide context, we are looking for obstructions to the existence of Kähler--Einstein metrics ...

### 5 References about conic bundles

I'm interested in stable rationality of conic bundles by means of Brauer group/unramified cohomology non-triviality, and I was wondering if there are some references for the basic properties of conic ...