Publications of the Research Institute for Mathematical Sciences
Noyabr 12, 202024.11.2020
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Publications of the Research Institute for Mathematical Sciences

   

J  – 2529

March 2020 No. 1  pp.1- 215  Vol. 56

Publ. KIMS Kyoto Univ. 56 (2020), 1-13

DOI 10.4171/PRIMS/56-1-1

Kahler Forms for Families of Calabi-Yau
Manifolds

by

Matthias Braun, Young-Jun Choi and Georg Schumacher

Abstract

      Kahler Einstein metrics for polarized families (/: X -> 5, Xx/S) of Calabi-Yau manifolds define a natural hermitian metric on the relative canonical bundle KX/s- The computa­tion of the curvature form being equal to the pullback of the Weil-Petersson form up to a numerical constant is used for the construction of a Kahler form on X, whose restriction to the fibers is Ricci flat.

2010 Mathematics Subject Classification: Primary 32G13; Secondary 53C55. Keywords: Moduli, Calabi- Yau manifolds, Weil-Petersson metric.