KAWA lecture notes on the Kähler-Ricci flow
arXiv:1508.04823 · doi:10.5802/afst.1571
Abstract
These lecture notes are based on a mini-course given by the author at the sixth KAWA Winter School on March 23-26, 2015 at the Centro De Giorgi of Scuola Normale Superiore in Pisa. They provide an introduction to the study of the Kahler-Ricci flow on compact Kahler manifolds, and a detailed exposition of some recent developments.
85 pages; final version to appear in Ann. Fac. Sci. Toulouse Math; corrected a few typos
References in corpus (9)
- The Kähler-Ricci flow on surfaces of positive Kodaira dimension
- Ricci flow and birational surgery
- Finite time collapsing of the Kähler-Ricci flow on threefolds
- Collapsing of Products Along the Kähler-Ricci Flow
- Soliton-type metrics and Kähler-Ricci flow on symplectic quotients
- Nakamaye's theorem on complex manifolds
- Teissier's problem on proportionality of nef and big classes over a compact Kähler manifold
- Convergence of Kähler-Ricci flow on lower dimensional algebraic manifolds of general type
- Geometric convergence of the Kähler-Ricci flow on complex surfaces of general type
Cited by in corpus (28)
- The Anomaly flow over Riemann surfaces
- Higher-order estimates for collapsing Calabi-Yau metrics
- Relative volume comparison of Ricci Flow and its applications
- Pluripotential kahler-ricci flows
- Smooth and Rough Positive Currents
- Local curvature estimates of long-time solutions to the Kähler-Ricci flow
- The Chern-Ricci flow
- The continuity method on minimal elliptic Kähler surfaces
- Geometry of twisted Kähler-Einstein metrics and collapsing
- Long time existence of the (n-1)-plurisubharmonic flow
- Convergence of the weak Kähler-Ricci Flow on manifolds of general type
- Kähler-Ricci flow on homogeneous toric bundles
- Canonical metric on moduli spaces of log Calabi-Yau varieties
- Parabolic complex Monge-Ampere equations on compact Kahler manifolds
- Leafwise flat forms on Inoue-Bombieri surfaces
- Collapsing immortal Kähler-Ricci flows
- Smooth approximation of the modified conical Kähler-Ricci flow
- Limit geometry of complete projective special real manifolds
- A note on conical Kähler-Ricci flow on minimal elliptic Kähler surfaces
- Independence of Singularity Type for Numerically Effective Kähler-Ricci Flows
- On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows
- Semipositive line bundles and (1,1)-classes
- Integral inequalities for holomorphic maps and applications
- Blowing up Chern-Ricci flat balanced metrics
- Remarks on the geodesic-Einstein metrics of a relative ample line bundle (with an appendix by Xu Wang)
- Convergence of cscK metrics on smooth minimal models of general type
- Pair-of-pants decompositions of 4-manifolds diffeomorphic to general type hypersurfaces
- Positivity in Foliated Manifolds and Geometric Applications