华罗庚青年数学论坛：Hyperbolicity for bases of families of higher dimensional manifolds

综合报告：

报告人：Dr. Ya Deng（University of Gothenburg）
      题  目：Hyperbolicity for bases of families of higher dimensional manifolds
      时  间：2019.08.26（星期一），13:30-14:30
      地  点：数学院晨兴110室
      摘  要: For maximally varying, smooth families of projective manifolds with semi-ample canonical bundle, the Shafarevich-Viehweg-Zuo hyperbolicity conjecture says that the base spaces of such families should be of log general type. This deep conjecture was proved by Campana-Paun in 2015, building on the previous fundamental work by Viehweg-Zuo in 2002. In Lecture 1, I will show that those base spaces are furthermore pseudo Kobayashi hyperbolic, i.e. Kobayashi hyperbolic modulo a proper closed Zariski subvariety, as predicted by the famous Lang conjecture. This in particular proves another conjecture by Viehweg-Zuo in 2003: moduli spaces of polarized manifolds with semi-ample canonical bundle are all Brody hyperbolic (no entire holomorphic curves). I will also present another related work (jointly with Dan Abramovich) on the Kobayashi hyperbolicity for bases of e？ectively smooth families of minimal general type manifolds. The main techniques rely on certain negatively twisted Higgs bundles initiated by Viehweg-Zuo in 2002 and the Finsler metric construction by To-Yeung and Schumacher.

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学术报告：

报告人：Dr. Ya Deng（University of Gothenburg）
      题  目：Kobayashi hyperbolicity for coarse moduli spaces and isotriviality of certain families
      时  间：2019.08.29（星期四），10:45-11:45
      地  点：数学院晨兴110室
      摘  要: 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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报告人：Dr. Ya Deng（University of Gothenburg）
      题  目：Strong positivity of the logarithmic cotangent bundles
      时  间：2019.08.29（星期四），16:00-17:00
      地  点：数学院晨兴110室
      摘  要: I will ？rst explain the “strongest positivity” which the logarithmic cotangent bundle of a log pair can possess. Then I will discuss a strategy to construct examples of log pairs whose log cotangent bundles have such strong positivity properties. These examples are constructed from any smooth n-dimensional complex projective varieties by considering the sum of at least n general su？ciently ample hypersurfaces. This result can be seen as a logarithmic counterpart of the Debarre conjecture, which was proved by Brotbek-Darondeau, Song-Yan Xie in 2015 independently. This work is jointly with Damian Brotbek.