Clemens's conjecture for rational curves on the generic quintic threefold
Let be a generic quintic threefold. A rational curve means a curve on birational to , and its degree is measured with respect to the embedding . Clemens's conjecture. The generic quintic threefold admits only a finite number of rational curves of each degree. Each rational curve is a smoothly embedded with normal bundle
Furthermore, all the rational curves on are mutually disjoint. This is the classical Clemens conjecture for the generic quintic threefold; the supplied passage gives no resolution status for the full statement.
References
Primary source
Rodolfo Aguilar, “The relative Clemens Conjectures for 12-log Calabi-Yau threefolds”, arXiv:2601.11813 (2026).
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