Filtrations and test-configurations: With an appendix by Sebastien Boucksom

Gábor Székelyhidi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


We introduce a strengthening of K-stability, based on filtrations of the homogeneous coordinate ring. This allows for considering certain limits of families of test-configurations, which arise naturally in several settings. We prove that if a manifold with no automorphisms admits a cscK metric, then it satisfies this stronger stability notion. We also discuss the relation with the birational transformations in the definition of $$b$$b-stability.

Original languageEnglish (US)
Pages (from-to)451-484
Number of pages34
JournalMathematische Annalen
Issue number1-2
StatePublished - Jun 1 2015

ASJC Scopus subject areas

  • Mathematics(all)


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