论文标题
部分可观测时空混沌系统的无模型预测
Normal Bundles of Rational Normal Curves on Hypersurfaces
论文作者
论文摘要
令$ c $为$ \ mathbb {p}^n $的合理普通曲线$ e $，然后让$ x \ subset \ subset \ mathbb {p}^n $为$ d $ d \ ge 2 $ Hypersurface co $ c $。在先前的工作中，I。Coskun和E. Riedl表明，普通捆绑包$ n_ {c/x} $对于一般$ x $是平衡的。 H. Larson研究了行的情况（$ e = 1 $），并计算了$ n_ {c/x} $具有给定的分裂类型的高空空间的维度。在本文中，我们使用任何$ e \ ge 2 $。我们计算所有可能的分裂类型的超曲面的显式示例，对于$ d \ ge 3 $，我们计算了$ n_ {c/x} $具有给定的分裂类型的高空空间的尺寸。对于$ d = 2 $，我们以固定分裂类型的最高级别给出了最高级别。
Let $C$ be the rational normal curve of degree $e$ in $\mathbb{P}^n$, and let $X\subset \mathbb{P}^n$ be a degree $d\ge 2$ hypersurface containing $C$. In previous work, I. Coskun and E. Riedl showed that the normal bundle $N_{C/X}$ is balanced for a general $X$. H. Larson studied the case of lines ($e=1$) and computed the dimension of the space of hypersurfaces for which $N_{C/X}$ has a given splitting type. In this paper, we work with any $e\ge 2$. We compute explicit examples of hypersurfaces for all possible splitting types, and for $d\ge 3$, we compute the dimension of the space of hypersurfaces for which $N_{C/X}$ has a given splitting type. For $d=2$, we give a lower bound on the maximum rank of quadrics with fixed splitting type.
