Cohomology of flag supervarieties and resolutions of determinantal ideals. II
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929651678445568 |
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| author | Sam, Steven V Snowden, Andrew |
| author_facet | Sam, Steven V Snowden, Andrew |
| contents | We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic or orthogonal group together with a semisimple representation of the periplectic Lie supergroup. The restriction of the latter to its even subgroup has an explicit multiplicity-free description in terms of Schur functors and is closely related to syzygies of (skew-)symmetric determinantal ideals. We develop tools for studying splitting rings for Coxeter groups of types BC and D, which may be of independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20797 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomology of flag supervarieties and resolutions of determinantal ideals. II Sam, Steven V Snowden, Andrew Algebraic Geometry Commutative Algebra Representation Theory We compute the coherent cohomology of the structure sheaf of complex periplectic Grassmannians. In particular, we show that it can be decomposed as a tensor product of the singular cohomology ring of a Grassmannian for either the symplectic or orthogonal group together with a semisimple representation of the periplectic Lie supergroup. The restriction of the latter to its even subgroup has an explicit multiplicity-free description in terms of Schur functors and is closely related to syzygies of (skew-)symmetric determinantal ideals. We develop tools for studying splitting rings for Coxeter groups of types BC and D, which may be of independent interest. |
| title | Cohomology of flag supervarieties and resolutions of determinantal ideals. II |
| topic | Algebraic Geometry Commutative Algebra Representation Theory |
| url | https://arxiv.org/abs/2412.20797 |