Log canonical models of elliptic surfaces
Log canonical models of elliptic surfaces
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DOI：
10.1016/j.aim.2017.08.035
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发表时间：
2016-10
期刊：
影响因子：
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通讯作者：
Kenneth Ascher;Dori Bejleri
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文献类型：
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作者：
Kenneth Ascher;Dori Bejleri
对椭圆曲面对（f：X→ C，S+ FA）的对数正则模型进行了分类，其中f：X→ C是椭圆纤维化，S是截面，FA是标记纤维的加权和.特别是，我们展示了对数正则模型如何依赖于权重的选择。我们描述了一个墙和室分解的空间的重量的基础上如何日志正则模型的变化。此外，我们还给出了带截面和标记纤维的椭圆曲面的标准丛的一个推广公式。这是利用极小模型程序构造椭圆曲面模空间紧化的第一步。
We classify the log canonical models of elliptic surface pairs (f: X→ C, S+ F A) where f: X→ C is an elliptic fibration, S is a section, and F A is a weighted sum of marked fibers. In particular, we show how the log canonical models depend on the choice of the weights. We describe a wall and chamber decomposition of the space of weights based on how the log canonical model changes. In addition, we give a generalized formula for the canonical bundle of an elliptic surface with section and marked fibers. This is the first step in constructing compactifications of moduli spaces of elliptic surfaces using the minimal model program.