Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces

Abstract

We exhibit families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding continuous surjective map from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds.

arXiv comment95 pages

References in corpus (3)

• Gravitational instantons with faster than quadratic curvature decay (II)
• Projective embedding of log Riemann surfaces and K-stability
• Volume estimates for Kähler-Einstein metrics and rigidity of complex structures

Cited by in corpus (15)

• Complex structure degenerations and collapsing of Calabi-Yau metrics
• SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family
• Special Lagrangian submanifolds of log Calabi-Yau manifolds
• Collapsing Ricci-flat metrics on elliptic K3 surfaces
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
• $S^1$-quotient of $Spin(7)$-structures
• Polystable log Calabi-Yau varieties and Gravitational instantons
• A Liouville theorem on asymptotically Calabi spaces
• Big Bang and Topology
• The SYZ mirror symmetry conjecture for del Pezzo surfaces and rational elliptic surfaces
• Spin(7) metrics from Kähler Geometry
• Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
• Global higher order estimates for collapsing Calabi-Yau metrics on elliptic K3 surfaces
• The Torelli Theorem for $AL{H}^{\ast }$ Gravitational Instantons