Kähler–Einstein metrics on Fano manifolds

By G. Tian. 2013

213 citations recorded by the source corpus.

This is an expository paper on Kähler metrics of positive scalar curvature. It is for my Takagi Lectures at RIMS in November of 2013. In this paper, I first discuss the Futaki invariants, the K-stability and its relation to the K-energy. Next I will outline my work in 2012 on the existence of Kähler–Einstein metrics on K-stable Fano manifolds. Finally, I will present S. Paul’s work on stability of pairs with some modifications of mine.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/17b5cd9c9306542386d6433a7b523671e9168f5d

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Kahler-Einstein metrics with edge singularities (2011, methodology): “, in particular, the papers [22], [51], [17], [18], [19], [63].”
Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II (2015, methodology): “Lemma 16, [10]) shows that iFh ≥ k−1ω−f2 ω for a smooth function f satisfying 0 ≤ f ≤ C and f converges to 0 uniformly on any compact subset of X \ ∪Fi.”
On the proper moduli spaces of smoothable Kähler–Einstein Fano varieties (2014, background): “, [9]–[11], [53])—is a major step forward, especially for understanding those Fano manifolds with Kähler–Einstein metrics.”
Kähler–Einstein metrics and volume minimization (2016, background): “In particular, the Yau–Tian–Donaldson correspondence has been established for smooth Fano manifolds (see in particular [57], [3], [16,58]).”
Kähler–Ricci flow, Kähler–Einstein metric, and K–stability (2015, methodology): “It also follows from [4] that in this case X is always K-semistable, and if X is K-stable, then X∞ = X , and X admits a Kähler-Einstein metric.”
Geometric pluripotential theory on Kähler manifolds (2019, background): “In particular, recent breakthroughs on K–stability (the work of Chen–Donaldson–Sun [38], Tian [107], Chen–Wang–Sun [40], Berman–Boucksom–Jonsson [10]) could not be presented, and we refer to [67, 108] for recent surveys on this topic.”