Repository logo
 

Gromov-Hausdorff collapsing of Calabi-Yau manifolds

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Gross, Mark 
Tosatti, Valentino 
Zhang, Yuguang 

Abstract

This paper is a sequel to Collapsing of Abelian Fibered Calabi-Yau Manifolds [12]. We further study Gromov–Hausdorff collapsing limits of Ricci-flat Kähler metrics on abelian fibered Calabi–Yau manifolds. Firstly, we show that in the same setup as Collapsing of Abelian Fibered Calabi-Yau Manifolds, if the dimension of the base manifold is one, the limit metric space is homeomorphic to the base manifold. Secondly, if the fibered Calabi–Yau manifolds are Lagrangian fibrations of holomorphic symplectic manifolds, the metrics on the regular parts of the limits are special Kähler metrics. By combining these two results, we extend Large complex structure limits of K3 surfaces [13] to any fibered projective K3 surface without any assumption on the type of singular fibers.

Description

Keywords

4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

COMMUNICATIONS IN ANALYSIS AND GEOMETRY

Conference Name

Journal ISSN

1019-8385
1944-9992

Volume Title

24

Publisher

International Press of Boston
Sponsorship
Mark Gross was supported in part by NSF grant DMS-1105871. Valentino Tosatti was supported in part by a Sloan Research Fellowship and NSF grant DMS-1236969. Yuguang Zhang was supported in part by NSFC-11271015.