A natural hermitian metric associated with local universal families of compact Kähler manifolds with zero first Chern class
Abstract
Let π : X → S be a local universal family of compact Kähler manifolds with zero first Chern class over a smooth base S. The complexified Kähler cones of each manifold of the family form a holomorphic fiber bundle K → S. We show that there exists a natural hermitian metric ω on the fiber product X×_{S} K. We then discuss the example of elliptic curves in some detail.
 Publication:

Comptes Rendus Mathematique
 Pub Date:
 January 2012
 DOI:
 10.1016/j.crma.2011.11.013
 arXiv:
 arXiv:1112.1343
 Bibcode:
 2012CRMat.350...63M
 Keywords:

 Mathematics  Algebraic Geometry;
 14
 EPrint:
 5 pages. This note is to appear in Comptes Rendus  Math\'ematique