AI 中文总结
该研究将Popa-Schnell的Viehweg双曲性成果推广到光滑Deligne-Mumford栈，证明参数化极大变差一般型代数簇族的光滑真DM栈的自然对数典范丛丰沛，并将结果应用于标准模空间。
AI 中文摘要
我们将Popa-Schnell关于光滑射影簇的Viehweg双曲性研究推广到光滑Deligne-Mumford栈的情形。Popa-Schnell的研究以Viehweg-Zuo的结果为基础，利用了Campana-Păun的结果，并扩展了Kebekus-Kovács和Patakfalvi的结果。我们证明，若具有射影粗模空间的光滑真DM栈参数化一族具有极大变差的一般型代数簇，则该栈的自然对数典范丛是丰沛的。我们还考虑了该栈的粗模空间的相关推论，并将结果应用于若干标准模空间。
英文摘要
We generalize work of Popa-Schnell on Viehweg hyperbolicity for smooth projective varieties to the case of smooth Deligne-Mumford stacks. The results of Popa-Schnell build on results of Viehweg-Zuo, utilize a result of Campana-Păun, and extend results of Kebekus-Kovács and Patakfalvi. We show that if a smooth proper DM stack with projective coarse moduli space parameterizes a family of varieties of general type having maximal variation, then the natural log canonical bundle of the stack is big. We also consider implications for the coarse moduli space of the stack, and apply the results to several standard moduli spaces.
Comments32 pages, AMS LaTeX
