TY - JOUR
T1 - Gromov-Hausdorff collapsing of Calabi-Yau manifolds
AU - Gross, Mark
AU - Tosatti, Valentino
AU - Zhang, Yuguang
N1 - Funding Information:
Supported in part by NSF grant DMS-1105871. Supported in part by a Sloan Research Fellowship and NSF grant DMS-1236969. Supported in part by NSFC-11271015
PY - 2016
Y1 - 2016
N2 - This paper is a sequel to [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 [12], 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 [13] to any fibered projective K3 surface without any assumption on the type of singular fibers.
AB - This paper is a sequel to [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 [12], 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 [13] to any fibered projective K3 surface without any assumption on the type of singular fibers.
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U2 - 10.4310/CAG.2016.v24.n1.a4
DO - 10.4310/CAG.2016.v24.n1.a4
M3 - Article
AN - SCOPUS:84976315933
SN - 1019-8385
VL - 24
SP - 93
EP - 113
JO - Communications in Analysis and Geometry
JF - Communications in Analysis and Geometry
IS - 1
ER -