锥连通流形
Conic-connected Manifolds
摘要：
我们研究一类特殊的有理连通流形，$X\subset \p^N$，使得两个一般点$x,x' \in X$可以通过包含在$X$中的二次曲线连接。我们证明了这些流形是Fano流形，且具有$b_2\leq 2$ .此外，对$b_2=2$进行了精确的分类。关于其多阶的高维完全相交提供了$b_2=1$情形的例子。分类结果的证明使用了合理性的一般表征，在合适的覆盖家庭的有理曲线。
英文摘要：
We study a particular class of rationally connected manifolds, $X\subset \p^N$, such that two general points $x,x' \in X$ may be joined by a conic contained in $X$. We prove that these manifolds are Fano, with $b_2\leq 2$. Moreover, a precise classification is obtained for $b_2=2$. Complete intersections of high dimension with respect to their multi-degree provide examples for the case $b_2=1$. The proof of the classification result uses a general characterization of rationality, in terms of suitable covering families of rational curves.
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