# Questions tagged [ag.algebraic-geometry]

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

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### Independent conditions imposed by a collection of double points

Let's consider the following statement : There exist a collection of $d$ points $\gamma \subset \mathbb{P}^{n}$, so that $h_{\Bbb P^n}(\gamma^{2} ,m) = \min\{(n+1)d, \binom {n+m}{n}\}$ implies for any ...
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### Is the schematic Fargues--Fontaine curve universally closed over $\mathbb{Q}_p$? [closed]

I have been thinking about this question and it appears that the so-called Fargues--Fontaine curve may be relevant. A definition is given in this document A curve is a regular, Noetherian, ...
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### Basic example of a formal affine scheme, functorial point of view

$\let\opn=\operatorname$For my BA thesis I have to describe formal groups from the functorial point of view. I am hence reading Strickland - Formal Schemes and Formal Groups, which is apparently the ...
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### Image of quasiprojective variety under closed map

Let $f: X\to Y$ be a regular map of projective varieties that is closed (in the sense that it takes Zariski closed sets to Zariski closed sets). Let $V\subset X$ be a quasiprojective subvariety (i.e. ...
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### Flat base change in the complex analytic setting

On page 255 of Hartshorne's Algebraic Geometry, it is shown that "cohomology commutes with flat base extension": Proposition III.9.3: Let $f : X \to Y$ be a separated morphism of finite type of ...
Let $f\colon X\to Y$ be a birational map of complex algebraic varieties. Are there necessarily open immersions of $X$ and $Y$ into varieties $X’$ and $Y’$, resp., which admit a proper morphism \$f’\...