On a conjecture of Oguiso about rational curves on Calabi-Yau threefolds
Simone Diverio, Andrea Ferretti

TL;DR
This paper proves that Calabi-Yau threefolds with a specific nef divisor and second Betti number greater than 4 necessarily contain rational curves, advancing understanding of their geometric structure.
Contribution
It establishes a new criterion linking nef divisors and the existence of rational curves on Calabi-Yau threefolds with high second Betti number.
Findings
Calabi-Yau threefolds with certain nef divisors contain rational curves
The second Betti number condition is crucial for the result
Provides insight into the geometry of Calabi-Yau threefolds
Abstract
Let X be a Calabi-Yau threefold. We show that if there exists on X a non-zero nef non-ample divisor then X contains a rational curve, provided its second Betti number is greater than 4.
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