Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 4

Special Issue: In Honor of Eduard Looijenga, Part 1 of 3

Guest Editor: Gerard van der Geer

Finiteness of rational curves of degree $12$ on a general quintic threefold

Pages: 537 – 557

DOI: http://dx.doi.org/10.4310/PAMQ.2015.v11.n4.a1

Authors

Edoardo Ballico (Dipartimento di Matematica, Università di Trento, Povo, TN, Italy)

Claudio Fontanari (Dipartimento di Matematica, Università di Trento, Povo, TN, Italy)

Abstract

We prove the following statement, predicted by Clemens’ conjecture: A generic quintic threefold contains only finitely many smooth rational curves of degree $12$.

Keywords

quintic threefold, rational curve, Clemens’ conjecture

Full Text (PDF format)