Local curvature estimates of long-time solutions to the Kähler-Ricci flow
arXiv:1903.05939
Abstract
We study the local curvature estimates of long-time solutions to the normalized Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundles. Using these estimates, we prove that on such a manifold, the set of singular fibers of the semi-ample fibration on which the Riemann curvature blows up at time-infinity is independent of the choice of the initial Kähler metric. Moreover, when the regular fiber of the semi-ample fibration is not a finite quotient of a torus, we determine the exact curvature blow-up rate of the Kähler-Ricci flow near the regular fiber.
arXiv commentSmall changes; accepted by Advances in Mathematics
References in corpus (13)
- The Kähler-Ricci flow on surfaces of positive Kodaira dimension
- Negative Holomorphic curvature and positive canonical bundle
- Adiabatic limits of Ricci-flat Kahler metrics
- An extension of a theorem of Wu-Yau
- KAWA lecture notes on the Kähler-Ricci flow
- The Collapsing Rate of the Kähler-Ricci Flow with Regular Infinite Time Singularity
- Remarks on the collapsing of torus fibered Calabi-Yau manifolds
- Lecture notes on the Kähler-Ricci flow
- Interior derivative estimates for the Kähler-Ricci flow
- Local Calabi and curvature estimates for the Chern-Ricci flow
- Relative volume comparison of Ricci Flow and its applications
- Convergence of scalar curvature of Kahler-Ricci flow on manifolds of positive Kodaira dimension
- Infinite-time singularity type of the Kähler-Ricci flow