Let be a Calabi#8211;Yau threefold. We show that if there exists on a non-zero nef non-ample divisor then contains a rational curve, provided its second Betti number is greater than 4.
Cite this article
Simone Diverio, Andrea Ferretti, On a conjecture of Oguiso about rational curves on Calabi–Yau threefolds. Comment. Math. Helv. 89 (2014), no. 1, pp. 157–172DOI 10.4171/CMH/315