Abstract
We construct a Kähler metric on the moduli spaces of compact complex manifolds with c1,<0 and of polarized compact Kähler manifolds with c1=0, which is a generalization of the Petersson-Well metric. It is induced by the variation of the Kähler-Einstein metrics on the fibers that exist according to the Calabi-Yau theorem. We compute the above metric on the moduli spaces of polarized tori and symplectic manifolds. It turns out to be the Maaß metric on the Siegel upper half space and the Bergmann metric on a symmetric space of type III resp. In particular it is Kähler-Einstein with negative curvature.
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Dedicated to Karl Stein
Heisenberg-Stipendiat der Deutschen Forschungsgemeinschaft
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Schumacher, G. On the geometry of moduli spaces. Manuscripta Math 50, 229–267 (1985). https://doi.org/10.1007/BF01168833
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DOI: https://doi.org/10.1007/BF01168833