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        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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        0answers
        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
        0answers
        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
        0answers
        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
        0answers
        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
        1answer
        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
        0answers
        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
        0answers
        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
        1answer
        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
        1answer
        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
        0answers
        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: ...
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        votes
        0answers
        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
        1answer
        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
        0answers
        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
        0answers
        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
        1answer
        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 ...

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