Families of canonically polarized varieties over surfaces
Families of canonically polarized varieties over surfaces
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表面上的正则极化品种族
DOI：
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发表时间：
2005
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通讯作者：
Sandor J. Kovacs
中科院分区：
文献类型：
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作者：
Stefan Kebekus;Sandor J. Kovacs
沙法列维奇的双曲猜想断言，准射影一维基底上的曲线族是等平凡的，除非基底的对数 Kodaira 维数为正。更一般地说，Viehweg 推测，如果正则极化变体的平滑家族具有最大变异，则该家族的基是对数一般类型。在本文中，我们将族的变化与基数的对数 Kodaira 维数联系起来，并对 Viehweg 关于由曲面参数化的族的猜想给出了肯定的答案。
Shafarevich’s hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More generally it has been conjectured by Viehweg that the base of a smooth family of canonically polarized varieties is of log general type if the family is of maximal variation. In this paper, we relate the variation of a family to the logarithmic Kodaira dimension of the base and give an affirmative answer to Viehweg’s conjecture for families parametrized by surfaces.