Work

Weighted extremal kähler metrics on resolutions of singularities

Year: 2025

Type: article

Abstract: Generalizing previous results of Arezzo–Pacard–Singer, Seyyedali–Székelyhidi, and Hallam, we prove the invariance under smooth blowups of the class of weighted extremal Kähler manifolds, modulo a log‐concavity assumption on the first weight. Through recent work of Di Nezza–Jubert–Lahdili and Han–Liu, this is obtained as a consequence of a general uniform coercivity estimate for the (relative, weighted) Mabuchi energy on the blowup, which applies more generally to any equivariant resolution of singularities of Fano type of a compact Kähler klt space whose Mabuchi energy is assumed to be coercive.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.70026

Authors: Sébastien Boucksom, Mattias Jonsson, Antonio Trusiani

Institutions: Centre National de la Recherche Scientifique, Université Paris Cité, Sorbonne Université, University of Michigan, University of Rome Tor Vergata

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Simons Foundation, Knut och Alice Wallenbergs Stiftelse

Awards: G1828992025, Non-Archimedean methods in complex analysis and geometry, Complex Analysis, Dynamics, and Geometry via Non-Archimedean Methods, G685656287