The continuity method on Fano fibrations

Abstract

We study finite-time collapsing limits of the continuity method. When the continuity method starting from a rational initial Kähler metric on a projective manifold encounters a finite-time volume collapsing, this projective manifold admits a Fano fibration over a lower dimensional base. In this case, we prove the continuity method converges to a singular Kähler metric on the base in the weak sense; moreover, if the base is smooth and the fibration has no singular fibers, then the convergence takes place in Gromov-Hausdorff topology.

V3, small changes; accepted by International Mathematics Research Notices

References in corpus (4)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• Finite time collapsing of the Kähler-Ricci flow on threefolds
• Bounding diameter of singular Kähler metric
• The Kähler-Ricci flow on Fano bundles

Cited by in corpus (1)

• On a twisted conical Kähler-Ricci flow