Minimal-volume canonical Calabi–Yau divisor conjecture

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Let s0=2s_0=2 and sm=sm−1(sm−1−1)+1s_m=s_{m-1}(s_{m-1}-1)+1 for m≥1m\geq 1 be Sylvester's sequence. For a positive integer nn, let XX be the nn-fold given by the canonical Calabi–Yau hypersurface construction in Proposition 1. Minimal-volume canonical Calabi–Yau divisor conjecture. The ample Weil divisor OX(1)\mathcal{O}_X(1) has minimal volume among all ample Weil divisors on canonical nn-folds XX satisfying KX∼Q0K_X\sim_{\mathbb{Q}}0. The conjecture is motivated by exact minimal-volume results for the cited low-dimensional cases, but its assertion in all dimensions remains open.

References

Primary source

Louis Esser, Burt Totaro and Chengxi Wang, “Varieties of general type with doubly exponential asymptotics”, arXiv:2109.13383 (2022).

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