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arXiv · 1111.4986

Filtrations and test-configurations

Gábor Székelyhidi
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Abstract

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-stability.

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Gábor Székelyhidi. 2011-11-21. Filtrations and test-configurations. https://arxiv.org/abs/1111.4986

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