We prove results on irreducibility of spaces of rational curves of low degree, and existence of rational curves with balanced normal bundle, on Fano hypersurfaces in projective space. The main method is to degenerate the hypersurface along with its ambient projective space to reducible varieties.

中文翻译：

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射影空间超曲面上的低阶有理曲线及其扇形退化

我们证明了在射影空间中的 Fano 超曲面上，低阶有理曲线空间的不可约性和具有平衡法丛的有理曲线的存在性的结果。主要方法是将超曲面及其周围的投影空间退化为可约变体。