Weighted Grassmannians and their explicit description
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914032854761472 |
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| author | Ovcharenko, Mikhail |
| author_facet | Ovcharenko, Mikhail |
| contents | We propose an explicit construction of a weighted generalised Grassmannian. For a weighted Grassmannian (i.e., for series A) we obtain an effective parametrisation of possible $\mathbb{Z}$-gradings on Plücker coordinates, and provide the explicit formulae for its dualising sheaf and Hilbert series in terms of this parametrisation. Our approach can be generalised to other irreducible root systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weighted Grassmannians and their explicit description Ovcharenko, Mikhail Algebraic Geometry Representation Theory 14M15 We propose an explicit construction of a weighted generalised Grassmannian. For a weighted Grassmannian (i.e., for series A) we obtain an effective parametrisation of possible $\mathbb{Z}$-gradings on Plücker coordinates, and provide the explicit formulae for its dualising sheaf and Hilbert series in terms of this parametrisation. Our approach can be generalised to other irreducible root systems. |
| title | Weighted Grassmannians and their explicit description |
| topic | Algebraic Geometry Representation Theory 14M15 |
| url | https://arxiv.org/abs/2501.15402 |