Extremal metrics on blowups along submanifolds

TL;DR

This paper establishes conditions for the existence of extremal Kähler metrics on blowups of manifolds along submanifolds of codimension greater than two, extending previous results from point blowups.

Contribution

It generalizes previous work by Arezzo-Pacard-Singer to higher codimension submanifolds, providing new criteria for extremal metric existence.

Findings

Conditions for extremal metrics on blowups along submanifolds

Extension of point blowup results to higher codimension

Broader applicability in Kähler geometry

Abstract

We give conditions under which the blowup of an extremal K\"ahler manifold along a submanifold of codimension greater than two admits an extremal metric. This generalizes work of Arezzo-Pacard-Singer, who considered blowups in points.