A Brody theorem for orbifolds

The Splitting Theorem for Orbifolds

An Algebraic Index Theorem for Orbifolds

Using the concept of a twisted trace density on a cyclic groupoid, a trace is constructed on a formal deformation quantization of a symplectic orbifold. An algebraic index theorem for orbifolds follows as a consequence of a local Riemann–Roch theorem for such densities. In the case of a reduced orbifold, this proves a conjecture by Fedosov, Schulze, and Tarkhanov. Finally, it is shown how the K...

Brody curves omitting hyperplanes

A Brody curve, a.k.a. normal curve, is a holomorphic map f from the complex line C to the complex projective space P such that the family of its translations {z 7→ f(z + a) : a ∈ C} is normal. We prove that Brody curves omitting n hyperplanes in general position have growth order at most one, normal type. This generalizes a result of Clunie and Hayman who proved it for n =

Multiplicity Formulas for Orbifolds Multiplicity Formulas for Orbifolds

Given a symplectic space, equipped with a line bundle and a Hamiltonian group action satisfying certain compatibility conditions, it is a basic question to understand the decomposition of the quantization space in irreducible representations of the group. We derive weight multiplicity formulas for the quantization space in terms of data at the fixed points on the symplectic space, which apply t...

Vector ultrametric spaces and a fixed point theorem for correspondences

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.