On the GIT quotient of Grassmannians by one dimensional torus
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917093025251328 |
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| author | Bonala, Narasimha Chary Kannan, S Senthamarai Pattanayak, Santosha |
| author_facet | Bonala, Narasimha Chary Kannan, S Senthamarai Pattanayak, Santosha |
| contents | We consider the action of the one-parameter subgroup of the special linear group corresponding to a simple root on Grassmannians and describe the structure of the associated Geometric Invariant Theory (GIT) quotients with respect to Plücker line bundle. Using the combinatorics of Weyl group elements, we explicitly describe the semistable loci and identify cases where the resulting quotient admits the structure of a parabolic induction of a projective space. We further analyze the orbit structure under the Levi subgroup, compute the Picard group, connected component of the automorphism group and examine key geometric features such as Fano properties, cohomology of line bundles, and projective normality with respect to the descended linearization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the GIT quotient of Grassmannians by one dimensional torus Bonala, Narasimha Chary Kannan, S Senthamarai Pattanayak, Santosha Algebraic Geometry 14L24, 14M15, 20G05 We consider the action of the one-parameter subgroup of the special linear group corresponding to a simple root on Grassmannians and describe the structure of the associated Geometric Invariant Theory (GIT) quotients with respect to Plücker line bundle. Using the combinatorics of Weyl group elements, we explicitly describe the semistable loci and identify cases where the resulting quotient admits the structure of a parabolic induction of a projective space. We further analyze the orbit structure under the Levi subgroup, compute the Picard group, connected component of the automorphism group and examine key geometric features such as Fano properties, cohomology of line bundles, and projective normality with respect to the descended linearization. |
| title | On the GIT quotient of Grassmannians by one dimensional torus |
| topic | Algebraic Geometry 14L24, 14M15, 20G05 |
| url | https://arxiv.org/abs/2511.15611 |