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Extremal metrics and K‐stability
Author(s) -
Székelyhidi Gábor
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl015
Subject(s) - mathematics , conjecture , scalar curvature , pure mathematics , algebraic geometry , invariant (physics) , geometric invariant theory , metric (unit) , variety (cybernetics) , computation , scalar (mathematics) , algebraic number , einstein , curvature , mathematical analysis , mathematical physics , geometry , statistics , algorithm , economics , differential equation , differential algebraic equation , ordinary differential equation , operations management
We propose an algebraic geometric stability criterion for a polarised variety to admit an extremal Kähler metric. This generalises conjectures by Yau, Tian and Donaldson, which relate to the case of Kähler–Einstein and constant scalar curvature metrics. We give a result in geometric invariant theory that motivates this conjecture, and an example computation that supports it.