A survey on symplectic singularities and symplectic resolutions
نویسندگان
چکیده
منابع مشابه
Counting resolutions of symplectic quotient singularities
Let Γ be a finite subgroup of Sp(V ). In this article we count the number of symplectic resolutions admitted by the quotient singularity V/Γ. Our approach is to compare the universal Poisson deformation of the symplectic quotient singularity with the deformation given by the Calogero-Moser space. In this way, we give a simple formula for the number of Q-factorial terminalizations admitted by th...
متن کاملRepresentations of Symplectic Reflection Algebras and Resolutions of Deformations of Symplectic Quotient Singularities
We give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products (with parameter t = 0) and the derived category of coherent sheaves on a crepant resolution of the spectrum of the centre of these algebras.
متن کاملA note on symplectic singularities
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...
متن کاملSymplectic 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...
متن کاملLocal Symplectic Algebra and Simple Symplectic Singularities of Curves
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales mathématiques Blaise Pascal
سال: 2006
ISSN: 1259-1734
DOI: 10.5802/ambp.218