snc klt KSBA稳定对的模空间自然是对数一般型的
Moduli spaces of snc klt KSBA stable pairs are naturally of log general type
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中文总结 AI 辅助
推广Wei-Wu关于稳定对族Viehweg双曲性工作至光滑Deligne-Mumford层，应用于参数化特定稳定对的光滑恰当模层，证明其有大对数典范丛，并探讨对粗模空间的影响。
中文摘要 AI 辅助
我们将Wei-Wu关于光滑射影簇上稳定对族的Viehweg双曲性的工作推广到光滑Deligne-Mumford层的情形。Wei-Wu的结果基于Popa-Schnell和Viehweg-Zuo的结果，利用了Campana-Păun的结果，并扩展了Kebekus-Kovács和Patakfalvi的结果。我们将结果应用于参数化一般klt相对简单正常交叉KSBA稳定对得光滑恰当模层，表明此类模层自然具有大对数典范丛。我们还考虑了其粗模空间的相关情况。
英文摘要
We generalize work of Wei-Wu on Viehweg hyperbolicity for families of stable pairs over smooth projective varieties to the case of smooth Deligne-Mumford stacks. The results of Wei-Wu build on results of Popa-Schnell and Viehweg-Zuo, utilize a result of Campana-Păun, and extend results of Kebekus-Kovács and Patakfalvi. We apply our results to smooth proper moduli stacks parameterizing generically klt relatively simple normal crossings KSBA stable pairs, showing that such moduli stacks naturally have big log canonical bundles. We also consider implications for their coarse moduli spaces.
