Initial degenerations of flag varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866918286430568448 |
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| author | Corey, Daniel Olarte, Jorge Alberto |
| author_facet | Corey, Daniel Olarte, Jorge Alberto |
| contents | We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal subdivisions of a suitable flag matroid polytope. As an application, we prove that the initial degenerations of $\operatorname{F\ell}^{\circ}(n)$ -- the open subvariety of the complete flag variety $\operatorname{F\ell}(n)$ consisting of flags in general position -- are smooth and irreducible when $n\leq 4$. We also study the Chow quotient of $\operatorname{F\ell}(n)$ by the diagonal torus of $\operatorname{PGL}(n)$, and show that, for $n=4$, this is a log crepant resolution of its log canonical model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_08094 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Initial degenerations of flag varieties Corey, Daniel Olarte, Jorge Alberto Algebraic Geometry Combinatorics 14T90 (primary) 14M15, 14C05, 52B20 (secondary) We prove that the initial degenerations of the flag variety admit closed immersions into finite inverse limits of flag matroid strata, where the diagrams are derived from matroidal subdivisions of a suitable flag matroid polytope. As an application, we prove that the initial degenerations of $\operatorname{F\ell}^{\circ}(n)$ -- the open subvariety of the complete flag variety $\operatorname{F\ell}(n)$ consisting of flags in general position -- are smooth and irreducible when $n\leq 4$. We also study the Chow quotient of $\operatorname{F\ell}(n)$ by the diagonal torus of $\operatorname{PGL}(n)$, and show that, for $n=4$, this is a log crepant resolution of its log canonical model. |
| title | Initial degenerations of flag varieties |
| topic | Algebraic Geometry Combinatorics 14T90 (primary) 14M15, 14C05, 52B20 (secondary) |
| url | https://arxiv.org/abs/2207.08094 |