On the Brody hyperbolicity of moduli spaces for canonically polarized manifolds

By E. Viehweg, K. Zuo. 2000

88 citations recorded by the source corpus.

We show that the moduli stack Mh of canonically polarized complex manifolds with Hilbert polynomial h is Brody hyperbolic. Hence if Mh denotes the corresponding coarse moduli scheme, and if U → Mh is a quasi-finite morphism, induced by a family, then there are no nonconstant holomorphic maps C→ U.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/28691072359311d1abc8e02339933a87c16c8b40

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In Geometry and Topology

1. Sai-Kee Yeung
2. Wing-Keung To
3. G. Schumacher
4. Liyou Zhang
5. Kang-Tae Kim
6. JongHae Keum

In Mathematical Physics

1. Sai-Kee Yeung
2. G. Schumacher
3. Wing-Keung To

Citations in the corpus

• Finsler metrics and Kobayashi hyperbolicity of the moduli spaces of canonically polarized manifolds (2015, methodology): “We also remark that as in [VZ03], Theorem 1 can be regarded as a result on the moduli stacks associated to the coarse moduli spaces of canoni-cally polarized manifolds.”
• Positivity of relative canonical bundles and applications (2012, result): “pencer tensors was derived. However, the curvature of the generalized Weil-Petersson metric seems not to satisfy any negativity condition. This difficulty was overcome in the work of Viehweg and Zuo in [V-Z1]. Their approach to hyperbolicity makes use of a period map. On the other hand our results are”