Holes in Calabi-Yau Effective Cones
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914386664226816 |
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| author | Gendler, Naomi Sheridan, Elijah Stillman, Michael Wu, David H. |
| author_facet | Gendler, Naomi Sheridan, Elijah Stillman, Michael Wu, David H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11173 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holes in Calabi-Yau Effective Cones Gendler, Naomi Sheridan, Elijah Stillman, Michael Wu, David H. High Energy Physics - Theory Algebraic Geometry 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. |
| title | Holes in Calabi-Yau Effective Cones |
| topic | High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2603.11173 |