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        Questions tagged [moduli-spaces]

        Given a concrete category C, with objects denoted Obj(C), and an equivalence relation ~ on Obj(C) given by morphisms in C. The moduli set for Obj(C) is the set of equivalence classes with respect to ~; denoted Iso(C). When Iso(C) is an object in the category Top, then the moduli set is called a moduli space.

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        votes
        0answers
        181 views

        Road map for moduli space/moduli problem/moduli stack

        I am familiar with (most of the) contents of Angelo Vistoli's notes on Descent theory (Stacks). I am also comfortable with basics of Schemes, their Cohomology (Cech), from Hartshorne's Algebraic ...
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        votes
        2answers
        319 views

        Moduli of curves over finite field

        This is related to this question. I learnt about moduli problem mainly with the book Harris and Morrison. Therefore, I have only seen the construction of moduli spaces $M_{g}$ over $\mathbb{C}$. But ...
        4
        votes
        1answer
        138 views

        Total Chern Class of Hodge Bundle via CohFT

        I am interested in the calculation of total Chern class of Hodge bundle. I am aware that there is a way by the Grothendieck-Riemann-Roch formula, however, I read that this is also a cohomological ...
        3
        votes
        0answers
        189 views

        Stacks in moduli spaces of sheaves research

        I want to get some practice and build more appreciation for the use of stacks in the context of classical moduli spaces of sheaves. Here by classical I vaguely mean hands-on description of the ...
        2
        votes
        1answer
        185 views

        Purity and skyscraper sheaves

        In "The Geometry of moduli spaces of sheaves" a coherent sheaf $\mathcal{F}$ is defined to be pure of dimension $d$ if dim$(\mathcal{E})=d$ for all non-trivial proper subsheaves $\mathcal{E} \subset \...
        2
        votes
        0answers
        105 views

        Coarse underlying curve of a smooth stable curve

        In the theory of moduli spaces of smooth stable curves with $n$-marked points, I have come across the notion of the coarse underlying curve. Let $C$ be a smooth stable genus $g$ curve with $n$-marked ...
        6
        votes
        1answer
        247 views

        Progress on Bondal–Orlov derived equivalence conjecture

        In their 1995 paper, Bondal and Orlov posed the following conjecture: If two smooth $n$-dimensional varieties $X$ and $Y$ are related by a flop, then their bounded derived categories of coherent ...
        2
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        0answers
        42 views

        Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant

        I am looking for the Picard group of the moduli space of semistable rank 2 parabolic vector bundles over smooth complex projective curves with trivial determinant. Having determinant trivial, I ...
        2
        votes
        1answer
        249 views

        Representability of Grassmannian functor by a scheme

        I am having some trouble following a proof that the Grassmannian functor is representable by a scheme. I am following the proof in EGA 9.7.4. It is only a small step that I am stuck on. For reference, ...
        1
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        0answers
        90 views

        Base change and family of stable maps

        Suppose that family F of stable maps given by maps $f:C \to S,\mu:C \to P^r$ and sections $\rho_i:S \to C$ Suppose that $\Sigma(F)$ be union of all one dimensional components of locus of nodes in ...
        5
        votes
        1answer
        180 views

        Coarse moduli space versus Kuranishi family

        We will work over complex number field $\mathbb{C}$. Let $\mathscr{M}_h$ be the moduli functor for canonically polarized manifolds with $h$ the Hilbert polynomial. Let us denote by $M_h$ the coarse ...
        1
        vote
        0answers
        83 views

        Log-canonical bundle of a smooth curve with marked points

        I am not sure if this question is appropriate for this site, but here it goes. I am not a geometer, so I am not familiar with notation in the area. I am interested in the moduli space of $r$-spin ...
        4
        votes
        1answer
        141 views

        Orientability of moduli space and determinant bundle of ASD operator

        Setting In instanton gauge theory, given a $G$-principal bundle $P\to X^4$, the orientability of the moduli space of ASD connections $$\mathcal{M}_k = \{A \in L^{2}_{k}(X, \Lambda^1 \otimes\mathrm{...
        6
        votes
        0answers
        56 views

        “Moduli space” of isotropic convex bodies?

        A lot of questions in convex geometry revolve around the geometry of isotropic convex bodies in $\mathbb{R^n}$. To my knowledge there is no, or very little study of a space such as : $$C_n = \{...
        3
        votes
        0answers
        80 views

        The moduli space of genus $0$ curves with $n$-punctures and complete linear systems on $\mathbb{P}_k^1$

        Let $\mathbb{P}_k^1$ be the projective line over an algebraically closed field $k$. The points of $(\Gamma(\mathbb{P}_k^1, \mathcal{O}_{\mathbb{P}_k^1}(n))-\{0\})/k^* = \mathbb{P}_k^n$ corresponds to ...

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