# Questions tagged [ag.algebraic-geometry]

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

15,167 questions

**5**

votes

**0**answers

82 views

### Original reference for Adams-Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^j(...

**2**

votes

**0**answers

35 views

### Varieties not injecting into liftable ones

I give you a finite field $F$. Can you give me an example of a geometrically connected smooth proper $F$-scheme $X$ such that there is no monomorphism (in the category of $F$-schemes) $X\rightarrow X'$...

**2**

votes

**0**answers

77 views

### A canonical complex computing etale cohomology

Crystalline cohomology can be computed as the hypercohomology of the de Rham-Witt complex.
If we want to compute the etale cohomology of the constant sheaves $\mathbb{Z}_l$ or $\mathbb{Q}_l$ (well, ...

**1**

vote

**0**answers

46 views

### Checking universal closedness on immersions

Let $X\rightarrow S$ be a morphism of schemes. Suppose that any $S$-immersion from $X$ to a separated $S$-scheme has a closed image. Is $X\rightarrow S$ universally closed?

**1**

vote

**1**answer

102 views

### Are there some relations between F-polynomials and theta functions?

F-polynomials are certain polynomials appears in the expansion formula of a cluster variable, see for example the formula (6.5) in cluster algebras IV. Theta functions in the paper correspond to ...

**4**

votes

**0**answers

210 views

### Rationally connected Kähler manifolds are projective

I would like to find a proof for Remark 0.5 in the following article of Claire Voisin:
https://webusers.imj-prg.fr/~claire.voisin/Articlesweb/fanosymp.pdf
She writes in this remark the following:
...

**4**

votes

**0**answers

120 views

### Non-artificial examples of “locally of finite type, but not quasi-compact”

Non-Noetherian objects do "arise in nature" (e.g. passing to infinite level in the perfectoid theory). The non-Noetherianity of perfectoids, if we employ the scheme-theoretic parlance, already occurs ...

**6**

votes

**1**answer

328 views

### Italian-style algebraic geometry in homotopy theory?

In homotopy theory, stacks can be occasionally useful (i.e. in the chromatic story). I come from a differential geometry background, so when people say that algebraic geometry is useful in homotopy ...

**2**

votes

**1**answer

131 views

### Pointless, non-singular, absolutely irreducible affine plane curves over finite fields

We think the following is true:
For all sufficiently large primes $p$ and all natural $g \ge 1$, there
exists affine plane curve $f(x,y)=0$ over $\mathbb{F}_p$ which
is non-singular, absolutely ...

**1**

vote

**0**answers

78 views

### Smooth absolutely irreducible (?) genus 1 plane pointless curve over $\mathbb{F}_{13}$

We got a family of genus 1 plane curves that may violate a bound
in a paper.
Explicitly: Let $F(x,y)$ be the degree 39 polynomial with integer coefficients:
...

**-3**

votes

**0**answers

72 views

### Complex Trigonometry Math Problem [on hold]

Problem Image
Hello everyone,
Does anybody know how to calculate the angle in the picture (REF 94.61) with all of the defined parameters (highlighted in red). If you do, could you show step by step ...

**1**

vote

**1**answer

121 views

### Bertini type theorem for very ample line bundle

Let $X$ be a normal, projective variety (can take $X$ to be a hypersurface in a projective space) of dimension at least $3$. Let $L$ be a very ample line bundle on $X$, hence base-point free. What can ...

**3**

votes

**0**answers

47 views

### How can I find the integral orthogonal group of a given symmetric positive definite form?

I wonder how one can study the integral orthogonal group of a given (symmetric, positive definite) bilinear form like the one described by the following matrix:
$$M=\begin{bmatrix}
x_1 &...

**6**

votes

**0**answers

73 views

### Catenarity and epimorphisms of rings

Let $R$ be a commutative ring. The following are well-known:
If $R$ is catenary and $\mathfrak{a}\subseteq R$ is an ideal, then $R/\mathfrak{a}$ is catenary.
If $R$ is catenary and $S\subseteq R$ is ...

**3**

votes

**1**answer

176 views

### Birational Invariants of regular surfaces

Let $X,Y$ surfaces (so $2$-dimensional proper $k$-schemes) which are regular (so the stalks are regular) and birational and denote by $f: X \dashrightarrow Y$ the corresponding rational birational ...