Reduced Delzant spaces and a convexity theorem

A Convexity Theorem and Reduced Delzant Spaces

The convexity theorem of Atiyah and Guillemin-Sternberg says that any connected compact manifold with Hamiltonian torus action has a moment map whose image is the convex hull of the image of the fixed point set. Sjamaar-Lerman proved that the Marsden-Weinstein reduction of a connected Hamitonian G-manifold is a stratified symplectic space. Suppose 1 → A → G → T → 1 is an exact sequence of compa...

Delzant models of moduli spaces

For every genus g, we construct a smooth, complete, rational polarized algebraic variety DMg together with a normal crossing divisor D = ⋃ Di, such that for every moduli space MΣ(2, 0) of semistable topologically trivial vector bundles of rank 2 on an algebraic curve Σ of genus g there exists a holomorphic isomorphism f : MΣ(2, 0) \ K2 → DMg \ D, where K2 is the Kummer variety of the Jacobian o...

Convexity and Geodesic Metric Spaces

In this paper, we first present a preliminary study on metric segments and geodesics in metric spaces. Then we recall the concept of d-convexity of sets and functions in the sense of Menger and study some properties of d-convex sets and d-convex functions as well as extreme points and faces of d-convex sets in normed spaces. Finally we study the continuity of d-convex functions in geodesic metr...

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.

Approximate Convexity and Submonotonicity in Locally Convex Spaces