An anticanonical perspective on G/P Schubert varieties
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916806408536064 |
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| author | Li, Changzheng Rietsch, Konstanze Yang, Mingzhi |
| author_facet | Li, Changzheng Rietsch, Konstanze Yang, Mingzhi |
| contents | We describe a natural basis of the Cartier class group of an arbitrary Schubert variety $X_{w,P}$ in a flag variety $G/P$ of general Lie type. We then characterise when the Schubert variety is factorial/Fano, along with an explicit formula for the anticanonical line bundle in these cases. We also prove that, for Schubert varieties in simply-laced types (only), being factorial is equivalent to being $Q$-factorial, and is equivalent to the equality of the Betti numbers $b_2(X_{w,P})=b_{2\ell(w)-2}(X_{w,P})$. Finally, we give a convenient characterisation of when a simply-laced Schubert variety is Gorenstein and when it is Gorenstein Fano. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An anticanonical perspective on G/P Schubert varieties Li, Changzheng Rietsch, Konstanze Yang, Mingzhi Algebraic Geometry 14M15 We describe a natural basis of the Cartier class group of an arbitrary Schubert variety $X_{w,P}$ in a flag variety $G/P$ of general Lie type. We then characterise when the Schubert variety is factorial/Fano, along with an explicit formula for the anticanonical line bundle in these cases. We also prove that, for Schubert varieties in simply-laced types (only), being factorial is equivalent to being $Q$-factorial, and is equivalent to the equality of the Betti numbers $b_2(X_{w,P})=b_{2\ell(w)-2}(X_{w,P})$. Finally, we give a convenient characterisation of when a simply-laced Schubert variety is Gorenstein and when it is Gorenstein Fano. |
| title | An anticanonical perspective on G/P Schubert varieties |
| topic | Algebraic Geometry 14M15 |
| url | https://arxiv.org/abs/2506.18388 |