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arXiv 1607.06149math.AG
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射影空间中有理曲线的法丛

Normal bundles of rational curves in projective space

Izzet Coskun, Eric Riedl

备注：
edited as per referee's comments
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摘要：

令$b_{\bullet}$为整数序列$1 < b_1 \leq b_2 \leq \cdots \leq b_{n-1}$。设$M(b_{\bullet})$是$\mathbb{P}^n$中具有普通奇点的非退化有理曲线，使得法丛具有分裂型$\bigoplus_{i=1}^{n-1}\mathcal{O}(e+b_i)$。当$n=3$时，Eisenbud，Van de Ven，Ghione和Sacchiero的著名结果表明$M(b_{\bullet})$是期望维数的不可约.我们表明，当$n \geq 5$，这些位点一般是可还原的组件高于预期的尺寸。我们给出的例子中，组件的数量与$n$线性增长。这些推广了Alzati和Re的一个例子。

英文摘要：

Let $b_{\bullet}$ be a sequence of integers $1 < b_1 \leq b_2 \leq \cdots \leq b_{n-1}$. Let $M(b_{\bullet})$ be the space parameterizing nondegenerate, rational curves of degree $e$ in $\mathbb{P}^n$ with ordinary singularities such that the normal bundle has the splitting type $\bigoplus_{i=1}^{n-1}\mathcal{O}(e+b_i)$. When $n=3$, celebrated results of Eisenbud, Van de Ven, Ghione and Sacchiero show that $M(b_{\bullet})$ is irreducible of the expected dimension. We show that when $n \geq 5$, these loci are generally reducible with components of higher than the expected dimension. We give examples where the number of components grows linearly with $n$. These generalize an example of Alzati and Re.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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