Balanced rational curves and minimal rational connectedness of Fano hypersurfaces
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 $\frac{(nd)(d\frac{5}{2})}{(n2)d}$.
 Publication:

arXiv eprints
 Pub Date:
 August 2020
 DOI:
 10.48550/arXiv.2008.01235
 arXiv:
 arXiv:2008.01235
 Bibcode:
 2020arXiv200801235R
 Keywords:

 Mathematics  Algebraic Geometry;
 14n25;
 14j45;
 14m22
 EPrint:
 arXiv admin note: text overlap with arXiv:2006.13375 Bug fixes from the last version. To appear in IMRN