Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Dr. Ya Deng, University of Gothenburg
Kobayashi hyperbolicity for coarse moduli spaces and isotriviality of certain families
Time & Venue:
2019.8.29 10:45-11:45 C110
I will present a recent work on the Kobayashi hyperbolicity of the coarse moduli spaces of canonically polarized or polarized Calabi-Yau manifolds in the sense of complex V -spaces (a generalization of the complex V -manifolds in the sense of Satake). As an application, I will show that, any smooth family of canonically polarized or polarized Calabi-Yau manifolds over a complex manifold with vanishing Kobayashi pseudo distance is necessarily isotrivial. This result can be seen as a hyperbolic version of Campana’s isotriviality conjecture, proved by Taji in 2015, stipulating that any smooth projective family of canonically polar-ized manifolds over “special manifold” (being opposite to general type manifolds introduced by Campana) is isotrivial.
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