A natural hermitian metric associated with local universal families of compact Ricci-flat Kähler manifolds

Gunnar Þór Magnússon

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arXiv · 1112.1343

A natural hermitian metric associated with local universal families of compact Ricci-flat Kähler manifolds

Gunnar Þór Magnússon

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Abstract

Let $π: \mathcal X \to S$ be a local universal family of compact Ricci-flat Kähler manifolds over a smooth base $S$. The complexified Kähler cones of each fiber of the family form a holomorphic fiber bundle $\mathcal K \to S$. We show that there exists a natural hermitian metric $ω$ on the fiber product $\mathcal X \times_S \mathcal K$. We then discuss the example of elliptic curves in some detail.

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Gunnar Þór Magnússon. 2011-12-06. A natural hermitian metric associated with local universal families of compact Ricci-flat Kähler manifolds. https://arxiv.org/abs/1112.1343

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