Variational and non-Archimedean aspects of the Yau--Tian--Donaldson conjecture

S\'ebastien Boucksom

Variational and non-Archimedean aspects of the Yau--Tian--Donaldson conjecture

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arxiv 1805.03289 v1 pith:5QM4HJAL submitted 2018-05-08 math.DG math.AGmath.CV

Sébastien Boucksom This is my paper · ORCID

classification math.DGmath.AGmath.CV

keywords conjecturek-stabilitynon-archimedeanahleralgebro-geometricaspectsconstantcurvature

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We survey some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature K\"ahler metrics to the algebro-geometric notion of K-stability. The emphasis is put on the use of pluripotential theory and the interpretation of K-stability in terms of non-Archimedean geometry.

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Analytic Bertini theorem II --- The local case
math.AG 2026-07 accept novelty 8.0 of 10

The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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