منابع مشابه
Symplectic surgeries from singularities
Given an isolated analytic hypersurface singularity 0 ∈ X0 := {f(z) = 0} ⊂ C one can form the smoothing Xt = {f(z) = t} and the resolution X̂ → X0, obtained by (repeatedly) blowing up the origin. These two associated spaces have the same link – that is, the intersection S ∩ f(0) – and there is a smooth surgery which replaces the smoothing by the resolution, or vice-versa. Thinking of the smoothi...
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It is proved that the diffeomorphism type of the minimal symplectic fillings of the link of a simple singularity is unique. In the proof, the uniqueness of the diffeomorphism type of CP 2 \D, where D is a pseudo holomorphic rational curve with one (2, 3)cusp, is discussed.
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Proof of Corollary 1. Assume that X has only terminal singularities. Then Codim(Σ ⊂ X) ≥ 3. By Theorem, Σ has no codimension 3 irreducible components. Therefore Codim(Σ ⊂ X) ≥ 4. Conversely, assume Codim(Σ ⊂ X) ≥ 4. Take a resolution f : Y → X of X and denote by {Ei} the f -exceptional divisors. Since X has canonical singularities, we have KY = f KX +ΣaiEi with non-negative integers ai. One can...
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We study the local symplectic algebra of parameterized curves introduced by V. I. Arnold in [A1]. We use the method of algebraic restrictions to classify symplectic singularities of quasi-homogeneous curves. We prove that the space of algebraic restrictions of closed 2-forms to the germ of a quasihomogeneous curve is a finite dimensional vector space. We also show that the action of local diffe...
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We generalize a theorem of Delzant classifying compact connected symplectic manifolds with completely integrable torus actions to certain singular symplectic spaces. The assumption on singularities is that if they are not finite quotient then they are isolated.
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ژورنال
عنوان ژورنال: Inventiones Mathematicae
سال: 2000
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s002229900043