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Tame stacks in positive characteristic
"... Since their introduction in [8, 4], algebraic stacks have been a key tool in the algebraic theory of moduli. In characteristic 0, one often is able to work with Deligne–Mumford stacks, which, especially in characteristic 0, enjoy a number of nice properties making them almost as easy to handle as al ..."
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Cited by 22 (7 self)
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Since their introduction in [8, 4], algebraic stacks have been a key tool in the algebraic theory of moduli. In characteristic 0, one often is able to work with Deligne–Mumford stacks, which, especially in characteristic 0, enjoy a number of nice properties making them almost as easy to handle as algebraic
On the geometry of DeligneMumford stacks
, 2006
"... Abstract. General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi)projective ” Deligne–Mumford stacks is identified, defined to be those that embed as a (locally) closed s ..."
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Cited by 4 (0 self)
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Abstract. General structure results about Deligne–Mumford stacks are summarized, applicable to stacks of finite type over a field. When the base field has characteristic 0, a class of “(quasi)projective ” Deligne–Mumford stacks is identified, defined to be those that embed as a (locally) closed substack of a smooth proper Deligne–Mumford stack having projective coarse moduli space. These conditions are shown to be equivalent to some wellstudied hypotheses. 1.
On the classification of rank two representations of quasiprojective fundamental groups
"... Abstract. Suppose X is a smooth quasiprojective variety over C and ρ: π1(X, x) → SL(2, C) is a Zariskidense representation with quasiunipotent monodromy at infinity. Then ρ factors through a map X → Y with Y either a DMcurve or a Shimura modular stack. 1. ..."
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Cited by 4 (2 self)
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Abstract. Suppose X is a smooth quasiprojective variety over C and ρ: π1(X, x) → SL(2, C) is a Zariskidense representation with quasiunipotent monodromy at infinity. Then ρ factors through a map X → Y with Y either a DMcurve or a Shimura modular stack. 1.
The orbifold cohomology ring of simplicial toric stack bundles
"... We introduce extended toric DeligneMumford stacks. We use an extended toric DeligneMumford stack to get the toric stack bundle and compute its orbifold Chow ring. Finally we generalize one result of Borisov, Chen and Smith so that the orbifold Chow ring of the toric stack bundle and the Chow ring ..."
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Cited by 4 (3 self)
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We introduce extended toric DeligneMumford stacks. We use an extended toric DeligneMumford stack to get the toric stack bundle and compute its orbifold Chow ring. Finally we generalize one result of Borisov, Chen and Smith so that the orbifold Chow ring of the toric stack bundle and the Chow ring of its crepant resolution are fibres of a flat family. 1
MCKAY’S CORRESPONDENCE FOR COCOMPACT DISCRETE SUBGROUPS OF SU(1, 1)
"... The classical McKay correspondence establishes an explicit link from the representation theory of a finite subgroup Π of SU(2) and the geometry of the minimal resolution of the affine surface V = C 2 /Π. In this paper we discuss a possible generalization of the McKay correspondence to the case when ..."
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The classical McKay correspondence establishes an explicit link from the representation theory of a finite subgroup Π of SU(2) and the geometry of the minimal resolution of the affine surface V = C 2 /Π. In this paper we discuss a possible generalization of the McKay correspondence to the case when Π is replaced with a discrete cocompact subgroup of the universal cover of SU(1, 1) such that its image Γ in PSU(1, 1) is a fuchsian group of signature (0, e1,..., en). We establish a correspondence between a certain class of finitedimensional unitary representations of Π and vector bundles on an algebraic surface with trivial canonical class canonically associated to Γ.
INSTANTONS AND FRAMED SHEAVES ON KÄHLER
"... Abstract. We provide stacky generalizations of classical gaugetheoretic results inspired by Donaldson, the UhlenbeckYau theorem and variants due to Bando and his collaborators. Moreover, we show an application of this machinery in the study of ALE spaces. Contents ..."
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Abstract. We provide stacky generalizations of classical gaugetheoretic results inspired by Donaldson, the UhlenbeckYau theorem and variants due to Bando and his collaborators. Moreover, we show an application of this machinery in the study of ALE spaces. Contents
THE AUTOMORPHISM GROUP OF TORIC
, 705
"... Abstract. We prove that the automorphism group of a toric DeligneMumford stack is isomorphic to the 2group associated to the stacky fan. 1. ..."
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Abstract. We prove that the automorphism group of a toric DeligneMumford stack is isomorphic to the 2group associated to the stacky fan. 1.
FOUNDATIONS OF TOPOLOGICAL STACKS I
, 2005
"... Abstract. This is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as far as introducing the homotopy groups and establish ..."
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Abstract. This is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as far as introducing the homotopy groups and establishing their basic properties. We also develop a Galois theory of covering spaces for a (locally connected semilocally 1connected) topological stack. Built into the Galois theory is a method for determining the stacky structure (i.e., inertia groups) of covering stacks. As a consequence, we get for free a characterization of topological stacks that are quotients of topological spaces by discrete group actions. For example, this give a handy characterization of good orbifolds. Orbifolds, graphs of groups, and complexes of groups are examples of topological (DeligneMumford) stacks. We also show that any algebraic stack (of finite type over C) gives rise to a topological stack. We also prove a Riemann Existence Theorem for stacks. In particular, the algebraic fundamental group
EXAMPLES OF ALGEBRAIC STACKS Contents
"... 2. Quotient stacks 1 3. Stacky curves 2 4. Actions of group(schemes) on algebraic stacks 2 ..."
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2. Quotient stacks 1 3. Stacky curves 2 4. Actions of group(schemes) on algebraic stacks 2