Kähler–Einstein metrics along the smooth continuity method
By V. Datar, G'abor Sz'ekelyhidi. 2015
132 citations recorded by the source corpus.
We show that if a Fano manifold M is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then M admits a Kähler–Einstein metric. This is a strengthening of the solution of the Yau–Tian–Donaldson conjecture for Fano manifolds by Chen–Donaldson–Sun (Int Math Res Not (8):2119–2125, 2014), and can be used to obtain new examples of Kähler–Einstein manifolds. We also give analogous results for twisted Kähler–Einstein metrics and Kahler–Ricci solitons.
Subfields: Applied Mathematics, Geometry and Topology, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/4ad0ee605a59566fac69c986b1b9bb6299d3c06f
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In Applied Mathematics
In Geometry and Topology
In Nuclear and High Energy Physics
Citations in the corpus
- On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, methodology): “ξ = Θ = 0), [33, 28, 9, 37, 72, 58, 80] for the twisted/conical Kähler-Einstein case (i.”
- Stability of valuations and Kollár components (2016, unknown): “ble if and only if any T-equivariant special test conguration (V; tc) !A1 of (V;) has nonnegative generalized Futaki invariant: Fut(V; tc) 0. When V is smooth and = 0, this follows from the work of [DS16] with an analytic argument. Our proof is completely algebraic. It again uses the techniques of d”
- Geodesic rays and stability in the cscK problem (2020, background): “Recently there have been significant progresses towards this conjecture, especially on the analytic part (see [6, 7, 24, 25, 26, 34]) and the Fano case ([27, 69, 30]).”
- A variational approach to the Yau–Tian–Donaldson conjecture (2015, methodology): “m pluripotential theory, lies in its relative simplicity. Our variational method easily extends to the setting of twisted Kahler-Einstein currents, and contains, in particular, the smooth setting in [DS16], as well as the log Fano case, at least as long Date: December 27, 2018. 1 arXiv:1509.04561v2 ”
- Algebraicity of the metric tangent cones and equivariant K-stability (2018, unknown): “he generalized Futaki invariant Fut(S,∆)˜ ≥0, and the equality holds only when the test configuration is a product, i.e. (S,∆)˜ ∼=(S,∆)×A1. Note that Theorem 1.4 is proved for smooth Fano manifolds in [DS16] for reductive group actions using analytic approach. Our result works for any singular Q-Fano”