The classification of weighted projective spaces

TL;DR

This paper classifies weighted projective spaces up to homeomorphism and homotopy equivalence, linking topological classifications with algebraic isomorphisms and demonstrating the rigidity of their Mislin genus.

Contribution

It provides two classifications of weighted projective spaces and establishes the equivalence with algebraic variety isomorphisms and the rigidity of their Mislin genus.

Findings

Classification up to homeomorphism matches algebraic isomorphism classification.

Weighted projective spaces have a rigid Mislin genus.

The paper links topological and algebraic classifications.

Abstract

We obtain two classifications of weighted projective spaces; up to homeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.