A generalization of Ross-Thomas' slope theory

Abstract

We give a formula of the Donaldson-Futaki invariants for certain type of semi test configurations, which essentially generalizes Ross-Thomas' slope theory. The positivity (resp. non-negativity) of those "a priori special" Donaldson-Futaki invariants implies K-stability (resp. K-semistability). We show its applicability by proving K-(semi)stability of certain polarized varieties with semi-log-canonical singularities, generalizing some results by Ross-Thomas.

15 pages. v2-4:minor changes, v5:re-edited (the latter half moved to arXiv:0807.1716 v5)

References in corpus (4)

• K-stability of constant scalar curvature polarization
• Special test configurations and $K$-stability of Fano varieties
• A stronger concept of K-stability
• The GIT-stability of Polarised Varieties via discrepancy

Cited by in corpus (44)

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• Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
• K-stability of Fano varieties: an algebro-geometric approach
• K-stability of log Fano hyperplane arrangements
• A valuative criterion for uniform K-stability of $\mathbb{Q}$-Fano varieties
• Kähler-Einstein metrics and volume minimization
• Wall crossing for K-moduli spaces of plane curves
• The GIT-stability of Polarised Varieties via discrepancy
• Weighted K-stability of polarized varieties and extremality of Sasaki manifolds
• Weighted K-stability and coercivity with applications to extremal Kahler and Sasaki metrics
• Uniform K-stability of polarized spherical varieties
• Hilbert-Mumford criterion for nodal curves
• On properness of K-moduli spaces and optimal degenerations of Fano varieties
• K-stability of Fano manifolds with not small alpha invariants
• On the limit of spectral measures associated to a test configuration
• Equivariant K-stability under finite group action
• Examples of K-unstable Fano manifolds with the Picard number one
• Openness results for uniform K-stability
• Alpha invariants and K-stability for general polarisations of Fano varieties
• On parametrization, optimization and triviality of test configurations
• Birational superrigidity and slope stability of Fano manifolds
• A Note on Equivariant K-stability
• Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
• Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
• On flops and canonical metrics
• Openness of uniform K-stability in the Kähler cone
• Deformation quantization and Kähler geometry with moment map
• Minimizing CM degree and slope stability of projective varieties
• Unstable polarized del Pezzo surfaces
• A decomposition formula for J-stability and its applications
• On K-stability of Calabi-Yau fibrations
• Sharp bounds on the height of K-semistable Fano varieties I, the toric case
• About J-flow, J-balanced metrics, uniform J-stability and K-stability
• Emergent complex geometry
• On log K-stability for asymptotically log Fano varieties
• Coupled Kähler-Einstein metrics
• Relative K-polystability of projective bundles over a curve
• Invariants of Varieties and Singularities inspired by Kahler-Einstein problems
• Stability of nets of quadrics in ${\mathbb{P}}^5$ and associated discriminants
• Separatedness of moduli of K-stable varieties
• On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line