Hyperplane Arrangements in the Grassmannian
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910106112753664 |
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| author | Mazzucchelli, Elia Pavlov, Dmitrii Wang, Kexin |
| author_facet | Mazzucchelli, Elia Pavlov, Dmitrii Wang, Kexin |
| contents | The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide a combinatorial formula, and explain how to compute this Euler characteristic in practice, both symbolically and numerically. Our particular focus is on generic hyperplane sections and on Schubert divisors. We also consider special Schubert arrangements relevant for physics. We study both the complex and the real case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_04288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperplane Arrangements in the Grassmannian Mazzucchelli, Elia Pavlov, Dmitrii Wang, Kexin Algebraic Geometry High Energy Physics - Theory Combinatorics 14M15, 14N10, 06A07, 05E99, 14Q15 The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide a combinatorial formula, and explain how to compute this Euler characteristic in practice, both symbolically and numerically. Our particular focus is on generic hyperplane sections and on Schubert divisors. We also consider special Schubert arrangements relevant for physics. We study both the complex and the real case. |
| title | Hyperplane Arrangements in the Grassmannian |
| topic | Algebraic Geometry High Energy Physics - Theory Combinatorics 14M15, 14N10, 06A07, 05E99, 14Q15 |
| url | https://arxiv.org/abs/2409.04288 |