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arXiv · 2603.11173

Holes in Calabi-Yau Effective Cones

Naomi Gendler·Elijah Sheridan·Michael Stillman·David H. Wu
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Abstract

Motivated by their role in non-perturbative potentials in string theory, we study divisors in effective cones of Calabi-Yau threefolds. We give examples of geometries for which some divisor classes in the effective cone are not themselves effective: i.e., they have no global sections. We call these non-holomorphic divisor classes "holes," and characterize their behavior in an ensemble of toric hypersurface Calabi-Yau threefolds. We prove some necessary and sufficient conditions for the existence of holes, show consequences of holes that follow from the minimal model program, and demonstrate that a class of holes come in semigroups (with this class conjectured to constitute all holes). Furthermore, we provide moduli-dependent bounds on the volumes of four-cycles representing holes.

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Naomi Gendler, Elijah Sheridan, Michael Stillman, David H. Wu. 2026-03-11. Holes in Calabi-Yau Effective Cones. https://arxiv.org/abs/2603.11173

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