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摘要翻译：
推广了著名的Shafarevich双曲性猜想，由Viehweg猜想，对于正则极化簇的模叠加，准射影流形允许一个泛有有限态射，它必然是对数广义型的。给出了一个映射到模叠加的拟射影曲面，利用对数复数形式的扩张性质，建立了模映射与曲面的极小模型程序之间的强关系。因此，我们可以很清楚地描述模量图所诱导的纤维化。作为一个推论，对Viehweg关于曲面上族的猜想有一个精炼的肯定的回答。
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英文标题：
《The structure of surfaces mapping to the moduli stack of canonically
polarized varieties》
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作者：
Stefan Kebekus and Sandor J. Kovacs
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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：
Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is necessarily of log general type. Given a quasi-projective surface that maps to the moduli stack, we employ extension properties of logarithmic pluri-forms to establish a strong relationship between the moduli map and the minimal model program of the surface. As a result, we can describe the fibration induced by the moduli map quite explicitly. A refined affirmative answer to Viehweg's conjecture for families over surfaces follows as a corollary.
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PDF链接：
https://arxiv.org/pdf/0707.2054
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