Obstructions to deforming curves on a prime Fano 3‐fold
Obstructions to deforming curves on a prime Fano 3‐fold
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素数 Fano 3 倍变形曲线的障碍
DOI：
10.1002/mana.201800185
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发表时间：
2019
影响因子：
1
通讯作者：
Nasu Hirokazu
中科院分区：
文献类型：
--
作者：
坊向伸隆;Nasu Hirokazu
我们证明了对于每个光滑素Fano 3-foldV，V上光滑连通曲线的Hilbert格式包含一个一般非约的Mumford型不可约分支。我们还研究了退化曲线CinV的变形，即，curvesC包含在一个光滑的anticanonical成员V。我们给出了C稳定退化的一个充分条件，即，CinV的每个小（和全局）变形都包含在SinV的变形中。因此，通过使用V的Hilbert-flag格式，我们确定了在点[C]处的维数和光滑性，假设Cin的类与V上的直线或圆锥曲线的类一起生成。
We prove that for every smooth prime Fano 3‐foldV, the Hilbert scheme of smooth connected curves onVcontains a generically non‐reduced irreducible component of Mumford type. We also study the deformations of degenerate curvesCinV, i.e., curvesCcontained in a smooth anticanonical member ofV. We give a sufficient condition forCto be stably degenerate, i.e., every small (and global) deformation ofCinVis contained in a deformation ofSinV. As a result, by using the Hilbert‐flag scheme ofV, we determine the dimension and the smoothness of at the point [C], assuming that the class ofCin is generated by together with the class of a line, or a conic onV.