Non-existence of smooth rational curves of degree d = 13, 14, 15 con-tained in a general quintic hypersurface of P4 and in some quadric hypersurface

Authors

  • E. Ballico

DOI:

https://doi.org/10.1285/i15900932v36n2p77

Keywords:

General quintic $3$-fold, rational curve, Clemens' conjecture

Abstract

Let $W \subset \mathbb {P}^4$ be a general quintic hypersurface. We prove that $W$ contains no smooth rational curve $C\subset \mathbb {P}^4$ with degree $d\in \{13,14,15\}$, $h^0(\mathcal {I} _C(1)) =0$ and $h^0(\mathcal {I} _C(2)) >0$.

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Published

21-12-2016

Issue

Volume 36, Issue 2 (2016)

Section

Articoli

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