A generalization of Ross-Thomas' slope theory
Yuji Odaka
TL;DR
This paper generalizes Ross-Thomas' slope theory by providing a formula for Donaldson-Futaki invariants of semi test configurations, linking their positivity to K-stability and applying it to varieties with semi-log-canonical singularities.
Contribution
It introduces a generalized formula for Donaldson-Futaki invariants applicable to semi test configurations, extending Ross-Thomas' slope theory and K-stability criteria.
Findings
Established K-(semi)stability for certain polarized varieties with semi-log-canonical singularities.
Generalized Ross-Thomas slope theory to broader classes of test configurations.
Connected positivity of invariants to K-stability and K-semistability.
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry