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Clemens's conjecture on high-dimensional components of rational-curve incidence spaces
Clemens's conjecture. Every component of $I_d$ of dimension at least $126$ projects under the natural map $I_d\to G$ to a subset of $G$ of positive codimension.
Conjectureopencalabi-yau-threefolds incidence-varieties rational-curvesarXiv posted 2 days ago

Clemens's conjecture on high-dimensional components of rational-curve incidence spaces