On the Moduli Space of Calabi-yau Manifolds
نویسنده
چکیده
Let X be a simply connected compact Kähler manifold with zero first Chern class, and let L be an ample line bundle over X. The pair (X,L) is called a polarized Calabi-Yau manifold. By a theorem of Mumford, the moduli space of the pair (X,L) (CY moduli) exists and is a complex variety. Locally, up to a finite cover, the moduli space is smooth (see [20, 21]). There is a natural Kähler metric, called the Weil-Petersson metric, on M. In this paper, we summarize and discuss the differential geometry of the couple (M, ωWP ), where ωWP is the Kähler form of the Weil-Petersson metric.
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