Triviality of fibered Calabi-Yau manifolds without singular fibers

Abstract

In this note we show that if a compact Kahler manifold with trivial canonical bundle is the total space of a holomorphic fibration without singular fibers, then the fibration is a holomorphic fiber bundle. In the algebraic case, the fibration becomes trivial after a finite base change.

11 pages; final version

References in corpus (1)

• Gromov-Hausdorff collapsing of Calabi-Yau manifolds

Cited by in corpus (7)

• The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
• Higher-order estimates for collapsing Calabi-Yau metrics
• Collapsing hyperkähler manifolds
• Geometry of twisted Kähler-Einstein metrics and collapsing
• A "boundedness implies convergence" principle and its applications to collapsing estimates in Kähler geometry
• Smooth asymptotics for collapsing Calabi-Yau metrics
• Ricci-flat metrics on Calabi-Yau manifolds