Filtrations and test-configurations

Details Filtrations and test-configurations Filtrations and test-configurations

2011-11-21

arxiv.org/abs/1111.4986v1

Mathematics

Algebraic Geometry

29 pages

Scientific paper

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 make some progress towards proving that if a manifold with no automorphisms admits a cscK metric, then it satisfies this stronger stability notion. Finally we discuss the relation with the birational transformations in the definition of b-stability.

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