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arXiv · 2008.01235

Balanced rational curves and minimal rational connectedness of Fano hypersurfaces

Ziv Ran
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Abstract

On a general Fano hypersurface in projective space, we determine for infinitely many $k$ the minimal degree $e$ of a rational curve through a general collection of $k$ points. In the case of a hypersurface of index 1, our results hold for all $k\geq 1$. In an appendix, M.C. Chang proves an arithmetical result which implies that in the case of index $>1$, the density of the set of curve degrees $e$ covered by our method is approximately $\frac{(n-d)(d-\frac{5}{2})}{(n-2)d}$.

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Ziv Ran. 2020-08-03. Balanced rational curves and minimal rational connectedness of Fano hypersurfaces. https://arxiv.org/abs/2008.01235

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