Abstract
In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus–Kovács conjecture Wei and Wu (Hyperbolicity for log smooth families with maximal variation, 2021), Conjecture 1.1, for smooth families of general type varieties as well as log smooth families of log canonical pairs of log general type, assuming the existence of relative good minimal models.
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Acknowledgements
We would like to thank Christian Schnell for useful discussions during the preparation of the paper. The first author also gets some inspiration from a workshop held in Shanghai Center for Mathematical Sciences.
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Wei, C., Wu, L. Isotriviality of smooth families of varieties of general type. manuscripta math. 172, 139–168 (2023). https://doi.org/10.1007/s00229-022-01394-y
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DOI: https://doi.org/10.1007/s00229-022-01394-y