摘要翻译：
设X是光滑复Fano变体。定义并研究了F:x->Y型光纤的拟初等收缩，其性质是rho(X)至多为rho(Y)+rho(F),其中rho是Picard数，F是F的一般光纤。特别地，纤维型的任何初等极值收缩都是拟初等的。我们证明了如果Y的维数最多为3，Picard数至少为4，则Y是光滑的和Fano的；另外，如果rho(Y)至少为6，则X为乘积。当dim(X)=4且X具有拟初等收缩时，这就给出了rho(X)的尖锐界，以及在高维中的其他应用。
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英文标题：
《Quasi elementary contractions of Fano manifolds》
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作者：
C. Casagrande
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最新提交年份：
2008
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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 X be a smooth complex Fano variety. We define and study 'quasi elementary' contractions of fiber type f: X -> Y. These have the property that rho(X) is at most rho(Y)+rho(F), where rho is the Picard number and F is a general fiber of f. In particular any elementary extremal contraction of fiber type is quasi elementary. We show that if Y has dimension at most 3 and Picard number at least 4, then Y is smooth and Fano; if moreover rho(Y) is at least 6, then X is a product. This yields sharp bounds on rho(X) when dim(X)=4 and X has a quasi elementary contraction, and other applications in higher dimensions.
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PDF链接：
https://arxiv.org/pdf/0704.3912