The Gauss-Bonnet Theorem for V-manifolds.

Satake, Ichirô

doi:10.2969/jmsj/00940464

Cited by 333 publications

(346 citation statements)

References 7 publications

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“…Since X is a smooth Deligne-Mumford stack with trivial generic stabilizer, it is the quotient of some algebraic space Z 1 by an action of GL(n 1 ) over k, by Edidin, Hassett, Kresch, and Vistoli ([8], Theorem 2.18). (In characteristic zero, this is essentially Satake's classical observation that an orbifold with trivial generic stabilizer is a quotient of a manifold by a compact Lie group, using the frame bundle corresponding to the tangent bundle ( [31], p. 475).)…”

Section: Lemma 71 Let X Be a Stack Of Finite Type Over A Locally Noementioning

confidence: 99%

The resolution property for schemes and stacks

Totaro¹

2004

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

109

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Section: Lemma 71 Let X Be a Stack Of Finite Type Over A Locally Noementioning

confidence: 99%

The resolution property for schemes and stacks

Totaro¹

2004

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

109

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“…Therefore, it is a rational number, which we will denote by ind orb (X). The orbifold Euler characteristic was defined by Satake in [25] using a triangulation, in analogy with the definition of the topological Euler characteristic of a manifold. It follows that the orbifold Euler characteristic of M is a rational number, which we will denote by χ orb (M ).…”

Section: Tensors On Orbifoldsmentioning

confidence: 99%

Compact anti-self-dual orbifolds with torus actions

Wright

2010

Sel. Math. New Ser.

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Abstract. We give a classification of toric anti-self-dual conformal structures on compact 4-orbifolds with positive Euler characteristic. Our proof is twistor theoretic: the interaction between the complex torus orbits in the twistor space and the twistor lines induces meromorphic data, which we use to recover the conformal structure. A compact anti-self-dual orbifold can also be constructed by adding a point at infinity to an asymptotically locally Euclidean (ALE) scalar-flat Kähler orbifold. We use this observation to classify ALE scalar-flat Kähler 4-orbifolds whose isometry group contain a 2-torus.

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“…B is a compact F-manifold of dimension two and is also a topological manifold. The quotient map n; M-^B is a F-bundle (see Satake [12] for definitions). Since M is compact, there are finitely many rotation leaves and dihedral leaves in F. Dihedral and reflection leaves correspond to the boundary points of B.…”

Section: Responding To Y=q Is L Q /G(l) Then There Is a C°° -Imbeddimentioning

confidence: 99%

Stability and Instability of Certain Foliations of 4-Manifolds by Closed Orientable Surfaces

Fukui¹

1986

Publ. Res. Inst. Math. Sci.

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Let FoI ff (M) denote the set of codimension q C°°-foliations of a closed m-manifold M. Fol^(M) carries a natural weak C r -topology (0 GL(q, JK) be the action determined from the linear holonomy of L, where q is the codimension of F. Then generalizing the results of Hirsch [7] and Thurston [16], Stowe [15] showed that if the cohomology group H^^L); R) is trivial, then F is C^stable. On the other hand, let F be the foliation of an orientable ^-bundle over a closed surface B by fibres. Seifert [13] showed that Fis C°-stable if z(l?)=i=0, where x(B) is the euler characteristic of B. The result was generalized by Fuller [6] to orientable circle bundles over arbitrary closed manifolds B with x(B)^F®. Langevin-Rosenberg [9] considered a fibration n: M-^B with fibre L and showed that the foliation of M by fibres is C°-stable provided that 1) n^LJ^Z, 2) B is a closed surface with 7(^)4=0 and 3) ^(J5) acts trivially on ^(X). The author [4] generalized the above result to compact codimension two foliations. Plante [10] classified all foliations of closed 3-manifolds by closed orientable surfaces into stable or unstable foliations. The author [5] classified all foliations of closed 3-manifolds by circles into stable or unstable foliations.

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The Gauss-Bonnet Theorem for V-manifolds.

Cited by 333 publications

References 7 publications

The resolution property for schemes and stacks

The resolution property for schemes and stacks

Compact anti-self-dual orbifolds with torus actions

Stability and Instability of Certain Foliations of 4-Manifolds by Closed Orientable Surfaces

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