JournalscmhVol. 89, No. 1pp. 157–172

On a conjecture of Oguiso about rational curves on Calabi–Yau threefolds

  • Simone Diverio

    Université Pierre et Marie Curie, Paris, France
  • Andrea Ferretti

    Université Lille 1, Villeneuve d'Ascq, France
On a conjecture of Oguiso about rational curves on Calabi–Yau threefolds cover
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Abstract

Let XX be a Calabi#8211;Yau threefold. We show that if there exists on XX a non-zero nef non-ample divisor then XX 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. 157–172

DOI 10.4171/CMH/315