J – 2529
March 2020 No. 1 pp.1- 215 Vol. 56
Publ. KIMS Kyoto Univ. 56 (2020), 1-13
Kahler Forms for Families of Calabi-Yau
Matthias Braun, Young-Jun Choi and Georg Schumacher
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.