Scholarlink

<p>We show that if a compact Kähler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo–Pacard–Singer and Székelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of Kähler–Ricci solitons and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2004_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>-cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Weighted Extremal Metrics on Blowups

  • 期刊论文

  • 发表日期：

    2025年5月6日

查看全文
  • Michael Hallam

摘要

We show that if a compact Kähler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo–Pacard–Singer and Székelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of Kähler–Ricci solitons and \(\mu \) μ -cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds.