Testing log K-stability by blowing up formalism
51 citations recorded by the source corpus.
We study logarithmic K-stability for pairs by extending the formula for Donaldson-Futaki invariants to log setting. We also provide algebro-geometric counterparts of recent results of existence of Kahler-Einstein metrics with cone singularities.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9a545e702f2288120ec385c43a41c4c11167c560
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In Applied Mathematics
- Robert J. Berman
- Chi Li
- S. Boucksom
- Mattias Jonsson
- Xiaowei Wang
- B. Berndtsson
- Tam'as Darvas
- Tomoyuki Hisamoto
In Geometry and Topology
- Robert J. Berman
- Chi Li
- S. Boucksom
- Mattias Jonsson
- B. Berndtsson
- Xiaowei Wang
- Tam'as Darvas
- Tomoyuki Hisamoto
Citations in the corpus
- Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties (2012, methodology): “clude some pathological phenomena observed in [42]. Similarly, if one also fixes a Q−divisor ∆ on X,with normal crossings, one can more generally define the log K-polystability of (X,L) wrt ∆ as before [31, 40, 45], but phrased in terms of the corresponding log Donaldson-Futaki invariants defined by f(”
- The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality (2012, background): “X;D/ (cf [20] and [28]).”
- Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs (2015, result): “This means that we reprove or slightly generalize some already known results [61, 63, 65, 66, 76].”
- K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, methodology): “hler-Einstein metrics has edge-cone singularities, even though the properness of the corresponding funtionals is not known. The notion of K-stability has also been generalized to the log setting (see [15, 21, 29]). Briefly, a test configuration for a log Fano variety (X,D) consists of a test configurat”
- Kahler-Einstein metrics on Fano manifolds, III: limits as cone angle approaches 2\pi\ and completion of the main proof (2013, unknown): “ily to the general case λ>1 with the Calabi-Yau metric replaced by a Kahler-Einstein metric on D(which exists because c1(D) <0). This Lemma also follows from the more general results [4], [29], [33]. Since we assume Xis K-stable, it follows that (X,D,β) is K-stable for any β∈ (0,1]. Step 6: No”