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Spain-P-P Κατάλογοι Εταιρεία
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Εταιρικά Νέα :
- REPRESENTABILITY OF HILBERT SCHEMES AND HILBERT STACKS OF POINTS - KTH
We show that the Hilbert functor of points on an arbitrary separated algebraic stack is an algebraic space We also show the al-gebraicity of the Hilbert stack of points on an algebraic stack and the algebraicity of the Weil restriction of an algebraic stack along a finite flat morphism
- Construction of Hilbert and Quot Schemes - arXiv. org
gave a sketch of the theory of descent, the construction of Hilbert and Quot schemes, and its application to the construction of Picard schemes (and also a sketch of formal schemes and some quotient techniques)
- Subsection 112. 5. 4 (04UZ): Quotient stacks—The Stacks project
A stack-theoretic proof of Luna's étale slice theorem is presented proving that for stacks $\mathcal{X} = [\mathop{\mathrm{Spec}}(A) G]$ with $G$ linearly reductive, then étale locally on the GIT quotient $\mathop{\mathrm{Spec}}(A^ G)$, $\mathcal{X}$ is a quotient stack by the stabilizer
- Lecture 6: The Hilbert and Quot schemes - Harvard University
represents the Hilbert functor HP X S More generally, if Eis a coherent sheaf on X, then there exists a projective S-scheme QuotP E,X S as well as a quotient sheaf qP E,X S: E QuotP E,X S!FP E,X S!0 on QuotP E,X S S X which is flat with proper support over Quot P E,X S and has Hilbert polynomial P such that the pair (QuotP E,X S,q P E,X S)
- Hilbert Schemes, Symmetric Quotient Stacks, and Categorical Heisenberg . . .
Hilbert scheme of points on X Example (n=2) : X[2]!X(2) is the blow-up along the diagonal Definition (General n) The Hilbert scheme (Douady space) X[n] is the fine moduli space of n-Clusters on X The Hilbert–Chow morphism : X[n]!X(n) sends an n-Cluster to its weighted support
- The construction of the Hilbert scheme - University of Illinois Chicago
THE HILBERT SCHEME Many important moduli spaces can be constructed as quotients of the Hilbert scheme by a group action For example, to construct the moduli space of smooth curves of genus g 2, we can rst embed all smooth curves of genus gin Pn(2 g2) by a su ciently large multiple of their canonical bundle Kn C Any automorphism of a variety
- A MODERN INTRODUCTION TO ALGEBRAIC STACKS
derived category of (quasi-)coherent sheaves on a stack, and the cotangent complex of a stack 1 ∞-Categories 1 1 Simplicial sets For every integer nE0, let [n] denote the nite set {0;1;:::;n} Let denote the category whose objects are the nite sets [n], for all nE0, and whose morphisms are order-preserving maps De nition 1 1
- The Hilbert Scheme of Points - SpringerLink
The Hilbert scheme of points \( \operatorname {\mathrm {Hilb}}^nS\), for S a projective nonsingular complex surface carrying a holomorphic symplectic 2-form (e g a K3 surface), is an irreducible holomorphic symplectic manifold, see Fujiki for n = 2 and Beauville for the general case
- HILBERT AND QUOT SCHEMES - ALGANT
As we will describe, to each closed sub-scheme X one can associate a k-rational point [X]d of a Grassmannian scheme (see section 1 4) It is called dth Hilbert point of X It can be shown that one also could recover X from [X]d, for d ≥ d0 := d0(X)
- Quotients of Schemes by Free Group Actions - MathOverflow
For any quasi-projective variety, there is a quasi-projective Hilbert scheme of $\lvert G \rvert$ points on $X$ For example, you can take the Hilbert scheme of points on the projective closure $\overline X$ and remove the closed subscheme of points which intersect $\overline X - X$
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