摘要翻译:
设F:x->Y是光滑基上正则极化复变体的光滑族。Viehweg推广了经典的Shafarevich双曲性猜想,猜想如果族具有最大变异,Y必然是对数广义型。作者在ARXIV:Math/0511378中证明了Viehweg猜想的一个更强和更精确的版本,其中Y是拟射影曲面。假设最小模型程序成立,本文对任意维数的射影基流形Y证明了同样的结果。
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英文标题:
《Families of varieties of general type over compact bases》
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作者:
Stefan Kebekus and Sandor 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:
Let f: X -> Y be a smooth family of canonically polarized complex varieties over a smooth base. Generalizing the classical Shafarevich hyperbolicity conjecture, Viehweg conjectured that Y is necessarily of log general type if the family has maximal variation. A somewhat stronger and more precise version of Viehweg's conjecture was shown by the authors in arXiv:math/0511378 in the case where Y is a quasi-projective surface. Assuming that the minimal model program holds, this very short paper proves the same result for projective base manifolds Y of arbitrary dimension.
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PDF链接:
https://arxiv.org/pdf/0704.2556