A Sheaf Cohomology Restriction Formula on Toric Complete Intersections
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913196413026304 |
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| author | Lyu, Zhentao |
| author_facet | Lyu, Zhentao |
| contents | We prove a sheaf cohomology restriction (SCORE) formula for a class of vector bundles on complete intersections in toric varieties. The formula enables one to compute cohomology products on the complete intersection $X$ via computations on the ambient space $V$ and potentially compute certain quantum corrections to the classical sheaf cohomology ring. Schematically the formula reads $(s_1,...,s_r)_X = (s_1,...,s_r, g)_V$ with $g$ being an explicitly described quantity derived from the monad data of the bundle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_07293 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Sheaf Cohomology Restriction Formula on Toric Complete Intersections Lyu, Zhentao Algebraic Geometry High Energy Physics - Theory K-Theory and Homology Rings and Algebras 14F06, 32L10, 55N45, 55N30 We prove a sheaf cohomology restriction (SCORE) formula for a class of vector bundles on complete intersections in toric varieties. The formula enables one to compute cohomology products on the complete intersection $X$ via computations on the ambient space $V$ and potentially compute certain quantum corrections to the classical sheaf cohomology ring. Schematically the formula reads $(s_1,...,s_r)_X = (s_1,...,s_r, g)_V$ with $g$ being an explicitly described quantity derived from the monad data of the bundle. |
| title | A Sheaf Cohomology Restriction Formula on Toric Complete Intersections |
| topic | Algebraic Geometry High Energy Physics - Theory K-Theory and Homology Rings and Algebras 14F06, 32L10, 55N45, 55N30 |
| url | https://arxiv.org/abs/2401.07293 |