Blow-up of a generalized flag variety
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909815978065920 |
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| author | Biswas, Indranil Saha, Pinakinath |
| author_facet | Biswas, Indranil Saha, Pinakinath |
| contents | Let $G$ be a connected simply connected semisimple complex algebraic group and $P\, \subset\, G$ a parabolic subgroup. We give a necessary and sufficient condition for a line bundle -- on the blow-up of the generalized flag variety $G/P$ along a smooth Schubert variety -- to be ample (respectively, nef). Furthermore, it is shown that every such nef line bundle is actually globally generated. As a consequence, we are able to describe when such a blow-up is (weak) Fano. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up of a generalized flag variety Biswas, Indranil Saha, Pinakinath Algebraic Geometry Representation Theory 14C20, 14M15, 14L30 Let $G$ be a connected simply connected semisimple complex algebraic group and $P\, \subset\, G$ a parabolic subgroup. We give a necessary and sufficient condition for a line bundle -- on the blow-up of the generalized flag variety $G/P$ along a smooth Schubert variety -- to be ample (respectively, nef). Furthermore, it is shown that every such nef line bundle is actually globally generated. As a consequence, we are able to describe when such a blow-up is (weak) Fano. |
| title | Blow-up of a generalized flag variety |
| topic | Algebraic Geometry Representation Theory 14C20, 14M15, 14L30 |
| url | https://arxiv.org/abs/2505.02203 |