# Questions tagged [ag.algebraic-geometry]

for questions on algebraic geometry, including algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

14,815 questions

**1**

vote

**0**answers

59 views

### Linear Morphism of Schemes

Let $U$ be an arbitrary scheme and we consider the schematic fiber product $\mathbb{A}^1 _U = \mathbb{A}^1 _{\mathbb{Z}} \times_{\mathbb{Z}} U$.
My question referer to Bosch's "linear morphisms" (of ...

**3**

votes

**0**answers

78 views

### $\infty$-categorical understanding of Bridgeland stability conditions?

On triangulated categories we have a notion of Bridgeland stability conditions.
Is there any known notion of "derived stability conditions" on a stable $\infty$ category $C$ such that they become ...

**3**

votes

**1**answer

55 views

### Topological realisation of a stack (explicit description)

Let $X$ be an Artin stack over $k=\mathbf{C}$. I've heard that $X$ has a topological realisation, but I've not been able to find an explicit decription.
My first guess would be: take a smooth cover $...

**4**

votes

**1**answer

197 views

### Applications of the idea of deformation in algebraic geometry and other areas?

The idea of proving something by deforming the general case to some special cases is very powerful. For example, one can prove certain equalities by regarding both sides as functions/sheaves, and show ...

**0**

votes

**0**answers

52 views

### Does positivstellensatz and SOS proof system help here?

I have a system of $m$ homogeneous degree $2$ polynomial equations in $\mathbb Z[x_1,\dots,x_n]$ where $m=poly(n)$. Take
$$f_1(x_1,\dots,x_n)=0$$
$$\dots$$
$$f_m(x_1,\dots,x_n)=0$$
to be the system.
...

**0**

votes

**0**answers

65 views

### When does the image of a morphism of schemes support scheme structure?

Let $Y$ be a qcqs scheme, $f:X\rightarrow Y$ be a quasi-compact morphism locally of finite presentation. Are there any conditions on $f$ which
do not force $f(X)$ be open or closed but force it to be ...

**1**

vote

**0**answers

45 views

### An injection from curve to projective plane is subscheme inclusion

Let $X$ be a connected scheme, $X\rightarrow \mathrm{Spec}\,\mathbb{C}$ be a morphism of finite type and relative dimension 1. Assume that there is a $\mathbb{C}$-morphism $f:X\rightarrow \mathbb{P}^2$...

**2**

votes

**0**answers

40 views

### Minimal Embedding for flags varieties

I would like to understand how to construct a parametization of a flag
variety $F(V,n_1,\ldots,n_r)\subseteq \mathbb{P}^N$ in its minimal embedding.
First, I would like to know if there is a closed ...

**3**

votes

**0**answers

85 views

### If there are nontrivial maps $H\mathbb{Z}^{top}\to MU$ then there are nontrivial maps $H\mathbb{Z}\to MGL$?

Let $H\mathbb{Z}^{top}$ be the Eilenberg-MacLane spectrum and $MU$ be the complex cobordism spectrum.
Consider now the motivic counterparts of the above spectral, namely $MGL$ (the motivic cobordism)...

**2**

votes

**0**answers

64 views

### The category of numerical motives over a finite field is generated by Artin motives and abelian varieties?

I heard from someone that people believe the category of numerical motives over a finite field is generated by Artin motives and abelian varieties.
What is the precise expection? How much do we know ...

**1**

vote

**0**answers

73 views

### Moduli space of almost complex structures as an algebro-geometric object

Let $M$ be a closed real-analytic manifold of dimension $2n$. Is it possible to make sense of the moduli space of real-analytic almost complex structures on $M$ as an algebro-geometric object (...

**3**

votes

**1**answer

111 views

### Non- simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their article 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as ...

**0**

votes

**0**answers

43 views

### Non-Compact Example where Putinar's Positivstellensatz Fails

One way to state Putinar's Positivstellensatz is as follows: a compact set polynomial inequalities $\mathcal{P} = \{P_1(x) \geq 0, \ldots, P_m(x) \geq 0\}$ is unsatisfiable if and only if there exists ...

**2**

votes

**0**answers

81 views

### Rationality of motivic zeta function for smooth Fano varieties

Assume the base field is complex number, and the coefficent is the Grothendieck ring of varieties (or it's localization at $[\mathbb L]$). We know the motivic zeta function for smooth projective ...

**0**

votes

**0**answers

95 views

### Do many homogeneous polynomials help in faster integer root extraction?

Given $n$ homogeneous algebraically independent total degree $2$ polynomials with no $x_1^2,\dots,x_n^2$ variable in $\mathbb Z[x_1,\dots,x_n]$ with promise that it has non-zero integer roots with ...