论文标题
对calabi-yau品种模量堆叠的双曲线的代数方法
An algebraic approach to the hyperbolicity of moduli stacks of Calabi-Yau varieties
论文作者
论文摘要
众所周知，Calabi-yau品种的模型堆都具有多种双曲线特性。迄今为止，使用复杂的Hodge理论等复杂的分析工具证明了最佳结果。尽管这种情况的积极特征截然不同（例如，主要极化的Abelian Vimension的模量至少2个包含有理曲线），但我们在本注中解释了如何通过将阳性特征降低到积极特征，最终依赖于Ogus和Vologodsky的积极特征来证明许多蜂房性的结果。
The moduli stacks of Calabi-Yau varieties are known to enjoy several hyperbolicity properties. The best results have so far been proven using sophisticated analytic tools such as complex Hodge theory. Although the situation is very different in positive characteristic (e.g. the moduli stack of principally polarized abelian varieties of dimension at least 2 contains rational curves), we explain in this note how one can prove many hyperbolicity results by reduction to positive characteristic, relying ultimately on the nonabelian Hodge theory in positive characteristic developed by Ogus and Vologodsky.
