Existence of Einstein Metrics on Fano Manifolds
By G. Tian. 2012
85 citations recorded by the source corpus.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/690b37a88f0131b00e97f79744d10fe6b628675b
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, methodology): “We refer to [77, 3, 79, 21, 80, 24, 9, 46, 59] for the KählerEinstein case (i.”
- On the moduli of Kähler-Einstein Fano manifolds (2012, background): “mstable (resp., Km-polystable, Km-semistable) for sufficiently divisible m∈ Z>0. The name “Km-stability” followed a suggestion of Donaldson in a discussion. The equivalent notion was also treated in [Tia12]. As we assumed Conjecture 1.5 for our π: X → S, we have a uniform lower bound for lct(Xs;−KX”
- Regularity of Kähler–Ricci flows on Fano manifolds (2013, background): “By extending the partial C-estimate conjecture [44] to the KählerRicci flow, one can show that these two approaches are actually equivalent (see Theorem 1.”
- Stability, birational transformations and the Kahler-Einstein problem (2010, result): “Hypotheses 1,3 and 4 are essentially known results, and very similar statements can be found in the recent paper [15] of Tian.”
- Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics (2012, background): “(X∞) = d. In [70] Tian found further constraints on the possible singularities that could appear in X∞. We will state a more general theorem and give an alternative proof. First we have (compare also [74]): Proposition 2.2 ([23]). Given a sequence of n-dimensional K¨ahler-Einstein Fano manifolds (Xi”
- K-polystability of Q-Fano varieties admitting Kähler-Einstein metrics (2012, methodology): “The existence of such a metric actually implies that the singularities are rather mild in the sense of the Minimal Model Program in birational geometry [4], more precisely the singularities of X are Kawamata log terminal (klt, for short), One motivation for considering the general singular setting i”
- Space of Ricci Flows I (2009, background): “This estimate then implies variety structure of limit space, as discussed in [108] and [49].”
- Special test configurations and $K$-stability of Fano varieties (2011, methodology): “ these results should also be considered as an evidence that the Gromov-Hausdroff limit of a family of Fano manifolds with KE metrics, which people conjecture to admit a complex analytic structure see [Tia10]), should be a Q-Fano variety with KE metric. Even more strongly, it suggests that the moduli”
- Integral bounds on curvature and Gromov–Hausdorff limits (2012, background): “ed by saying that things work out in the way that one might at first sight guess at. As we have mentioned before, the proofs of many of the statements, given Theorem 1.1, have been outlined by Tian in [23]. Thus we view this Section, broadly speaking, as an opportunity to attempt a careful exposition”
- The partial $C^0$-estimate along the continuity method (2013, methodology): “As explained in [44], the partial C -estimate allows us to compare the Mabuchi energy of the metrics ωt with the Bergman metrics obtained using embeddings with L(2)-orthonormal sections.”