Equivariant Alexandrov Geometry and Orbifold Finiteness

Orbifold Homeomorphism Finiteness Based on Geometric Constraints

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold homeomorphism types. This is a generalization to the orbifold category of a similar result for manifolds proven by Grove, Petersen, and Wu. It follows that any Laplace ...

Equivariant Algebraic Geometry

Holomorphic symplectic geometry and orbifold singularities

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 Nakam...

Twisted Einstein Tensors and Orbifold Geometry

Following recent advances in the local theory of current-algebraic orbifolds, we study various geometric properties of the general WZW orbifold, the general coset orbifold and a large class of (non-linear) sigma model orbifolds. Phase-space geometry is emphasized for the WZW orbifolds – while for the sigma model orbifolds we construct the corresponding sigma model orbifold action, which include...

Equivariant Localization: BV-geometry and Supersymmetric Dynamics

It is shown, that the geometrical objects of Batalin-Vilkovisky formalism– odd symplectic structure and nilpotent operator ∆ can be naturally uncorporated in Duistermaat–Heckman localization procedure. The presence of the supersymmetric bi-Hamiltonian dynamics with even and odd symplectic structure in this procedure is established. These constructions can be straightly generalized for the path-...