ALE scalar-flat K\"ahler metrics on non-compact weighted projective spaces

TL;DR

This paper constructs explicit scalar-flat Kähler ALE metrics on non-compact weighted projective spaces and uses them to derive smooth extremal Kähler metrics on resolutions of orbifolds, advancing geometric analysis in complex geometry.

Contribution

It introduces new explicit toric scalar-flat Kähler ALE metrics on non-compact weighted projective spaces and applies these to obtain extremal metrics on resolutions of orbifolds.

Findings

Constructed explicit toric scalar-flat Kähler ALE metrics.

Derived smooth extremal Kähler metrics on resolutions of orbifolds.

Extended the class of known extremal metrics on weighted projective spaces.

Abstract

We construct new explicit toric scalar-flat K{\"a}hler ALE metrics on weighted projective spaces of non-compact type, which we use to obtain smooth extremal K{\"a}hler metrics on appropriate resolutions of orbifolds. In particular, we obtain new extremal metrics certain resolutions of weighted projective spaces of compact type.