$SL(2,\mathbb{C})$特征簇的对数卡拉比-丘紧化
Log Calabi-Yau compactifications of $SL(2,\mathbb{C})$ character varieties
AI总结：
本文证明紧定向曲面及带孔曲面的$SL(2,\mathbb{C})$特征簇可实现特定对数卡拉比-丘紧化，建立仿射簇紧化为对数卡拉比-丘的充分条件，并验证了相关文献构造的紧化满足要求。
AI中文摘要：
我们证明，紧定向曲面的$SL(2,\mathbb{C})$特征簇，以及带孔曲面的一般相对$SL(2,\mathbb{C})$特征簇，均允许除子对数终端（dlt）对数卡拉比-丘紧化。为此，我们建立了一个一般性结果，给出由仿射簇的正则函数代数的滤子得到的紧化为对数卡拉比-丘的充分条件。随后，我们将该结果应用于证明，Kutteri-Tehrani-Frohman构造的紧情形紧化，以及Tehrani-Frohman构造的带孔情形紧化，均为对数典范且对数卡拉比-丘。
英文摘要：
We prove that the $SL(2,\mathbb{C})$ character varieties of compact oriented surfaces and the generic relative $SL(2,\mathbb{C})$ character varieties of punctured surfaces admit divisorial log terminal (dlt) log Calabi-Yau compactifications. To do this, we establish a general result giving sufficient conditions for a compactification of an affine variety arising from a filtration of its algebra of regular functions to be log Calabi-Yau. We then apply this result to show that the compactifications constructed by Kutteri-Tehrani-Frohman in the compact case and by Tehrani-Frohman in the punctured case are log canonical and log Calabi-Yau.
