共查询到20条相似文献,搜索用时 15 毫秒
1.
Jarod Alper 《Journal of Pure and Applied Algebra》2010,214(9):1576-1591
We show that near closed points with linearly reductive stabilizer, Artin stacks are formally locally quotient stacks by the stabilizer. We conjecture that the statement holds étale locally and we provide some evidence for this conjecture. In particular, we prove that if the stabilizer of a point is linearly reductive, the stabilizer acts algebraically on a miniversal deformation space, generalizing the results of Pinkham and Rim. We provide a generalization and stack-theoretic proof of Luna’s étale slice theorem which shows that GIT quotient stacks are étale locally quotients stacks by the stabilizer. 相似文献
2.
Masao Aoki 《manuscripta mathematica》2006,121(1):135-56
We study Hom 2-functors parameterizing 1-morphisms of algebraic stacks, and prove that they are representable by algebraic
stacks under certain conditions, using Artin's criterion. As an application we study Picard 2-functors which parameterize
line bundles on algebraic stacks.
An erratum to this article is available at . 相似文献
3.
Kai A. Behrend 《Advances in Mathematics》2005,198(2):583-622
We introduce the notion of cofoliation on a stack. A cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism. Cofoliations are uniquely determined by their associated Lie algebroids.Cofoliations on stacks arise from flat connections on groupoids. Connections on groupoids generalize connections on gerbes and bundles in a natural way. A flat connection on a groupoid is an integrable distribution of the morphism space compatible with the groupoid structure and complementary to both source and target fibres. A cofoliation of a stack determines the flat groupoid up to étale equivalence.We show how a cofoliation on a stack gives rise to a refinement of the Hodge to De Rham spectral sequence, where the E1-term consists entirely of vector bundle valued cohomology groups.Our theory works for differentiable, holomorphic and algebraic stacks. 相似文献
4.
Takehiko Yasuda 《Advances in Mathematics》2006,207(2):707-761
The aim of this article is to develop the theory of motivic integration over Deligne-Mumford stacks and to apply it to the birational geometry of Deligne-Mumford stacks. 相似文献
5.
Indranil Biswas 《Advances in Mathematics》2008,219(4):1150-1176
Let C be a smooth projective curve of genus g?2 over a field k. Given a line bundle L on C, let Sympl2n,L be the moduli stack of vector bundles E of rank 2n on C endowed with a nowhere degenerate symplectic form up to scalars. We prove that this stack is birational to BGm×As for some s if deg(E)=n⋅deg(L) is odd and C admits a rational point P∈C(k) as well as a line bundle ξ of degree 0 with ξ⊗2?OC. It follows that the corresponding coarse moduli scheme of Ramanathan-stable symplectic bundles is rational in this case. 相似文献
6.
Sharon Hollander 《Mathematische Zeitschrift》2011,269(1-2):467-494
We study properties of morphisms of stacks in the context of the homotopy theory of presheaves of groupoids on a small site . There is a natural method for extending a property P of morphisms of sheaves on to a property ${\mathcal{P}}$ of morphisms of presheaves of groupoids. We prove that the property ${\mathcal{P}}$ is homotopy invariant in the local model structure on when P is stable under pullback and local on the target. Using the homotopy invariance of the properties of being a representable morphism, representable in algebraic spaces, and of being a cover, we obtain homotopy theoretic characterizations of algebraic and Artin stacks as those which are equivalent to simplicial objects in satisfying certain analogues of the Kan conditions. The definition of Artin stack can naturally be placed within a hierarchy which roughly measures how far a stack is from being representable. We call the higher analogues of Artin stacks n-algebraic stacks, and provide a characterization of these in terms of simplicial objects. A consequence of this characterization is that, for presheaves of groupoids, n-algebraic is the same as 3-algebraic for all n ≥ 3. As an application of these results we show that a stack is n-algebraic if and only if the homotopy orbits of a group action on it is. 相似文献
7.
We construct new “virtually smooth” modular compactifications of spaces of maps from nonsingular curves to smooth projective toric varieties. They generalize Givental's compactifications, when the complex structure of the curve is allowed to vary and markings are included, and are the toric counterpart of the moduli spaces of stable quotients introduced by Marian, Oprea, and Pandharipande to compactify spaces of maps to Grassmannians. A brief discussion of the resulting invariants and their (conjectural) relation with Gromov-Witten theory is also included. 相似文献
8.
Given a pair of G-covering functors F1:R→R1 and F0:R→R0 such that F0 is a Galois covering, the inequality for all z,t, of the dimensions of the first kind module sets under some assumptions is proved (Theorem 2.2). The result is applied to show the equality of the module variety dimensions for some special degenerations of algebras. Certain consequences for preserving wild and tame representation types by G-covering functors are also presented (Theorems 2.4 and 3.1). 相似文献
9.
Daniel Naie 《Expositiones Mathematicae》2013,31(1):40-72
A formula for the irregularity of abelian coverings of smooth projective surfaces is established. Explicit computations are performed and some applications are presented. 相似文献
10.
Dominic Joyce 《Advances in Mathematics》2006,203(1):194-255
This is the first in a series of papers on configurations in an abelian category A. Given a finite partially ordered set (I,?), an (I,?)-configuration(σ,ι,π) is a finite collection of objects σ(J) and morphisms ι(J,K) or π(J,K):σ(J)→σ(K) in A satisfying some axioms, where J,K are subsets of I. Configurations describe how an object X in A decomposes into subobjects, and are useful for studying stability conditions on A.We define and motivate the idea of configurations, and explain some natural operations upon them—subconfigurations, quotient configurations, substitution, refinements and improvements. Then we study moduli spaces of (I,?)-configurations in A, and natural morphisms between them, using the theory of Artin stacks. We prove well-behaved moduli stacks exist when A is the abelian category of coherent sheaves on a projective scheme P, or of representations of a quiver Q.In the sequels, given a stability condition (τ,T,?) on A, we will show the moduli spaces of τ-(semi)stable objects or configurations are constructible subsets in the moduli stacks of all objects or configurations. We associate infinite-dimensional algebras of constructible functions to a quiver Q using the method of Ringel-Hall algebras, and define systems of invariants of P that ‘count’ τ-(semi)stable coherent sheaves on P and satisfy interesting identities. 相似文献
11.
12.
We prove various properties of varieties of special linear systems on double coverings of hyperelliptic curves. We show and determine the irreducibility, generically reducedness and singular loci of the variety for bi-elliptic curves and double coverings of genus two curves. Similar results for double coverings of hyperelliptic curves of genus h≥3 are also presented. 相似文献
13.
In this paper we consider the curves defined over and give a positive answer to a conjecture about a divisibility condition on L-polynomials of the curves . Our proof involves finding an exact formula for the number of -rational points on for all n, and uses a result we proved elsewhere about the number of rational points on supersingular curves. 相似文献
14.
15.
We show that the orbifold Chow ring of a root stack over a well-formed weighted projective space can be naturally seen as
the Jacobian algebra of a function on a singular variety. 相似文献
16.
It is well known that the number of unramified normal coverings of an irreducible complex algebraic curve C with a group of covering transformations isomorphic to Z2⊕Z2 is (24g−3⋅22g+2)/6. Assume that C is hyperelliptic, say . Horiouchi has given the explicit algebraic equations of the subset of those covers which turn out to be hyperelliptic themselves. There are of this particular type. In this article, we provide algebraic equations for the remaining ones. 相似文献
17.
A finite simplicial graph Γ determines a right-angled Artin group GΓ, with generators corresponding to the vertices of Γ, and with a relation υw=wυ for each pair of adjacent vertices. We compute the lower central series quotients, the Chen quotients, and the (first) resonance
variety of GΓ, directly from the graph Γ.
Partially supported by NSF grant DMS-0311142. 相似文献
18.
Matthew Satriano 《Mathematische Zeitschrift》2013,274(3-4):779-804
We develop a theory of toric Artin stacks extending the theories of toric Deligne–Mumford stacks developed by Borisov–Chen–Smith, Fantechi–Mann–Nironi, and Iwanari. We also generalize the Chevalley–Shephard–Todd theorem to the case of diagonalizable group schemes. These are both applications of our main theorem which shows that a toroidal embedding $X$ is canonically the good moduli space (in the sense of Alper) of a smooth log smooth Artin stack whose stacky structure is supported on the singular locus of $X$ . 相似文献
19.
Isamu Iwanari 《Comptes Rendus Mathematique》2010,348(19-20):1107-1109
In this Note we show that an Artin stack with finite inertia stack is étale locally isormorphic to the quotient of an affine scheme by an action of a general linear group. 相似文献
20.
We study the module category of a certain Galois covering of a cluster-tilted algebra which we call the cluster repetitive algebra. Our main result compares the module categories of the cluster repetitive algebra of a tilted algebra C and the repetitive algebra of C, in the sense of Hughes and Waschbüsch. 相似文献