A generalization of the Ross--Thomas slope theory

By Y. Odaka. 2009

143 citations recorded by the source corpus.

We give a formula for the Donaldson–Futaki invariants of certain type of semi test configurations, which essentially generalizes the Ross–Thomas slope theory [28]. The positivity (resp. non-negativity) of those “a priori special” Donaldson–Futaki invariants implies K-stability (resp. K-semistability). As an application, we prove the K-(semi)stability of certain polarized varieties with semi-log-canonical singularities, which generalizes some results of [28].

View Paper: https://www.semanticscholar.org/paper/98b59924b1c55c289ff4643bd936d55e02cfdbe9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Y. Odaka
2. Robert J. Berman
3. S. Boucksom
4. Yuji Sano
5. Chi Li
6. R. Dervan
7. Chenyang Xu
8. Mattias Jonsson

Citations in the corpus

• Kähler metrics with constant weighted scalar curvature and weighted K‐stability (2018, unknown): “Our inspiration comes mainly from the recent works [27, 28, 39] which, in turn, build on the seminal work of Tian [83, 85] and a key observation by Wang [88] and Odaka [70, 71] that the Donaldson–Futaki invariant of a (suitably compactified) test configuration can be realized as an intersection numb”
• Optimal destabilizing centers and equivariant K-stability (2020, unknown): “[34,42]) Assume π : (X , tc;L) → A1 is a G-equivariant test configuration of (X, ; L).”
• Uniform K-stability and asymptotics of energy functionals in Kähler geometry (2016, background): “llow from the discussion in [BHJ15, x7.3] and from [BHJ15, Proposition 3.15], respectively. Note that intersection theoretic formulas for the DonaldsonFutaki invariant appeared already in [Wan12] and [Oda13]. For a general non-Archimedean metric ˚on Lwe can dene DF(˚) = MNA(˚) + V 1 (X 0 X 0;red) Ln”
• Alpha invariant and K-stability of Q-Fano varieties (2010, methodology): “Let us start from recalling the formula from [23].”
• K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, background): “5.2. Towards the case of Q−Fano varieties. Let us finally discuss some of the new complicationsthat arisewhen trying to generalizeTian’s programto the case of singular K-polystable Fano varieties X(by [51] such a Fano variety Xautomatically has log terminal singularities). Taking ηto be a smooth semi”
• Kähler–Einstein metrics and volume minimization (2016, unknown): “nd only if (X× C1,I D×C1 ·I δ·(t)c) is sub log canonical. Thus we have the identity: lct(Xν,Dν−∆ (Xν,Dν;ν∗L);X ν 0 ) = lct(X×C1,ID×C1 ·I δ;(t)). The rest of the argument is the same as in [Fuj15] and [Oda13]. Assume (X,D) is a log pair such that L= −δ−1(KX+D) is an ample Cartier divisor. Denote by S”