Holomorphic symplectic geometry and orbifold singularities
نویسنده
چکیده
Let G be a finite group acting on a symplectic complex vector space V . Assume that the quotient V/G has a holomorphic symplectic resolution. We prove that G is generated by “symplectic reflections”, i.e. symplectomorphisms with fixed space of codimension 2 in V . Symplectic resolutions are always semismall. A crepant resolution of V/G is always symplectic. We give a symplectic version of Nakamura conjectures.
منابع مشابه
Automatic Transversality and Orbifolds of Punctured Holomorphic Curves in Dimension Four
We derive a numerical criterion for J–holomorphic curves in 4–dimensional symplectic cobordisms to achieve transversality without any genericity assumption. This generalizes results in [HLS97] and [IS99] to allow punctured curves with boundary that generally need not be somewhere injective or immersed. As an application, we combine this with the intersection theory of punctured holomorphic curv...
متن کاملOrbifold Cohomology of ADE-singularities
We study Ruan’s cohomological crepant resolution conjecture [39] for orbifolds with transversal ADE singularities. In the An-case we compute both the orbifold cohomology ring H ∗ orb([Y ]) and the quantum corrected cohomology ring H(Z)(q1, ..., qn). The former is achieved in general, the later up to some additional, technical assumptions. We construct an explicit isomorphism between H orb([Y ])...
متن کاملA Gluing Construction for Holomorphic Spheres and Symplectic Vortices
We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regular stable symplectic vortices on a fixed curve with varying markings has the structure of a stratified-smooth topological orbifold. In addition, we show that the moduli space has a non-canonical Corbifold structure.
متن کاملQuestions about cobordism of symplectic and toric manifolds
1 Toric varieties are by now familiar objects in algebraic geometry, but this note is concerned with variations on that theme, and I will try to be careful about terminology. A toric variety is a kind of orbifold, and hence has mild singularities, but I will use the term toric manifold in the sense of Davis and Januszkiewicz [4]; a smooth toric variety thus has an underlying toric manifold, but...
متن کاملDeformations of Symplectic Vortices
We prove a gluing theorem for a symplectic vortex on a compact complex curve and a collection of holomorphic sphere bubbles. Using the theorem we show that the moduli space of regular strongly stable symplectic vortices on a fixed curve with varying markings has the structure of a stratified-smooth topological orbifold. In addition, we show that the moduli space has a non-canonical C -orbifold ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999