Semi-ampleness conjecture for nef integral divisors on Calabi–Yau threefolds
A SCY3 is a smooth Calabi–Yau threefold. A divisor is nef if its intersection with every curve is nonnegative, and an integral divisor is one whose class is integral. A divisor is semi-ample if some positive multiple is base-point-free.
Semi-ampleness conjecture. Any nef integral divisor on a SCY3 is semi-ample.
This is described as a notoriously difficult open conjecture. It concerns the relationship between numerical positivity and the existence of morphisms on Calabi–Yau threefolds.
References
Primary source
Keiji Oguiso, “Automorphisms of Calabi-Yau threefolds from algebraic dynamics and the second Chern class”, arXiv:2407.17297 (2024).
Additional references
4 papers in this index state this conjecture (2010–2024). The statement above is taken from the most recent of them; the others are arXiv:1201.1130, arXiv:1003.1388, arXiv:1003.1483.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
Solutions 0
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