TY - JOUR
T1 - Filtrations and test-configurations
T2 - With an appendix by Sebastien Boucksom
AU - Székelyhidi, Gábor
N1 - Funding Information:
I would like to thank Jeff Diller, Simon Donaldson, Sonja Mapes and Jacopo Stoppa for useful conversations. I am also grateful for Sebastien Boucksom providing the proof of Theorem B as an appendix to this paper. This work was partially supported by NSF grant DMS-0904223.
Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2015/6/1
Y1 - 2015/6/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00208-014-1126-3
DO - 10.1007/s00208-014-1126-3
M3 - Article
AN - SCOPUS:84939993045
SN - 0025-5831
VL - 362
SP - 451
EP - 484
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 1-2
ER -