The Kähler-Ricci flow and optimal degenerations

DOI10.4310/jdg/1599271255zbMath1447.53081arXiv1612.07299OpenAlexW3083570392WikidataQ115164813 ScholiaQ115164813MaRDI QIDQ2199669

Gábor Székelyhidi, Ruadhaí Dervan

Publication date: 14 September 2020

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07299

zbMATH Keywords

Fano manifoldKähler-Einstein metricsDonaldson-Futaki invariant\(H\)-functional

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Fano varieties (14J45) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)

Related Items (26)

The existence of the Kähler–Ricci soliton degeneration ⋮ Tian's partial \(C^0\)-estimate implies Hamilton-Tian's conjecture ⋮ Generalized Kähler-Ricci flow on toric Fano varieties ⋮ Equivariant \(\mathbb{R}\)-test configurations and semistable limits of \(\mathbb{Q}\)-Fano group compactifications ⋮ Diameter estimates for long-time solutions of the Kähler-Ricci flow ⋮ Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties ⋮ Kähler-Ricci flow on Fano manifolds ⋮ Geometric flow, multiplier ideal sheaves and optimal destabilizer for a Fano manifold ⋮ Algebraic geometry: moduli spaces, birational geometry and derived aspects. Abstracts from the workshop held July 10--16, 2022 ⋮ Mabuchi's soliton metric and relative D-stability ⋮ Kähler–Ricci flow on homogeneous toric bundles ⋮ Calabi type functionals for coupled Kähler-Einstein metrics ⋮ Toric geometry. Abstracts from the workshop held March 27 -- April 2, 2022 ⋮ Global pluripotential theory over a trivially valued field ⋮ The Kähler-Ricci flow and quantitative bounds for Donaldson-Futaki invariants of optimal degenerations ⋮ Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry ⋮ Collapsing of the line bundle mean curvature flow on Kähler surfaces ⋮ Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow ⋮ On sharp lower bounds for Calabi-type functionals and destabilizing properties of gradient flows ⋮ Thresholds, valuations, and K-stability ⋮ Valuative invariants with higher moments ⋮ The inverse Monge-Ampère flow and applications to Kähler-Einstein metrics ⋮ Uniformly strong convergence of Kähler-Ricci flows on a Fano manifold ⋮ The moduli space of Fano manifolds with Kähler-Ricci solitons ⋮ Optimal destabilization of K-unstable Fano varieties via stability thresholds ⋮ Kähler-Ricci flow for deformed complex structures

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