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arXiv · 1705.08441

Normal bundles of rational curves on complete intersections

Izzet Coskun·Eric Riedl
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Abstract

Let $X \subset \mathbb{P}^n$ be a general Fano complete intersection of type $(d_1,\dots, d_k)$. If at least one $d_i$ is greater than $2$, we show that $X$ contains rational curves of degree $e \leq n$ with balanced normal bundle. If all $d_i$ are $2$ and $n\geq 2k+1$, we show that $X$ contains rational curves of degree $e \leq n-1$ with balanced normal bundle. As an application, we prove a stronger version of the theorem of Z. Tian \cite{Tian}, Q. Chen and Y. Zhu \cite{ChenZhu} that $X$ is separably rationally connected by exhibiting very free rational curves in $X$ of optimal degrees.

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Izzet Coskun, Eric Riedl. 2017-05-23. Normal bundles of rational curves on complete intersections. https://arxiv.org/abs/1705.08441

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