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摘要翻译：
本文在合理的假设下证明了一维复圆盘上Kodaira维数为零的曲面的射影对数极小退化的Euler特征公式，并作为其应用，确定了阿贝尔和超椭圆情形下对数极小退化的奇性。通过利用Fujino-Mori的广义正则丛公式对奇异纤维的局部分析进行全局化，我们将abelian fibred Calabi-Yau的奇异纤维个数从上面三倍地束缚了下来，这是Oguiso以前在潜在良好的归约情况下所做的。
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英文标题：
《The Euler Characteristic Formula for Logarithmic Minimal Degenerations
of Surfaces with Kodaira Dimension Zero and its application to Calabi-Yau
Threefolds with a pencil》
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作者：
Koji Ohno
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper, the Euler characteristic formula for projective logarithmic minimal degenerations of surfaces with Kodaira dimension zero over a 1-dimensional complex disk is proved under a reasonable assumption and as its application, the singularity of logarithmic minimal degenerations are determined in the abelian or hyperelliptic case. By globalizing this local analysis of singular fibres via generalized canonical bundle formulae due to Fujino-Mori, we bound the number of singular fibres of abelian fibred Calabi-Yau threefolds from above,which was previously done by Oguiso in the potentially good reduction case.
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PDF链接：
https://arxiv.org/pdf/0710.3641
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