关于具有不可分裂控制族有理曲线的Fano流形
On Fano manifolds with an unsplit dominating family of rational curves
摘要：
研究了含有不可分裂控制族有理曲线的Fano流形$X$，证明了当$X$具有伪指标$i_X = (\dim X)/3$或维数$\dim X=6$时，广义Mukai猜想成立.我们还证明了这个猜想对所有具有$i_X > (\dim X)/3$的Fano流形都成立。
英文摘要：
We study Fano manifolds $X$ admitting an unsplit dominating family of rational curves and we prove that the Generalized Mukai Conjecture holds if $X$ has pseudoindex $i_X = (\dim X)/3$ or dimension $\dim X=6$. We also show that this conjecture is true for all Fano manifolds with $i_X > (\dim X)/3$.
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