Moduli Spaces of Hyperplanar Admissible Flags in Projective Space
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909336619450368 |
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| author | Cooper, George |
| author_facet | Cooper, George |
| contents | We prove the existence of quasi-projective coarse moduli spaces parametrising certain complete flags of subschemes of a fixed projective space $\mathbb{P}(V)$ up to projective automorphisms. The flags of subschemes being parametrised are obtained by intersecting non-degenerate subvarieties of $\mathbb{P}(V)$ of dimension $n$ by flags of linear subspaces of $\mathbb{P}(V)$ of length $n$, with each positive dimension component of the flags being required to be non-singular and non-degenerate, and with the dimension $0$ components being required to satisfy a Chow stability condition. These moduli spaces are constructed using non-reductive Geometric Invariant Theory for actions of groups whose unipotent radical is graded, making use of a non-reductive analogue of quotienting-in-stages developed by Hoskins and Jackson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02453 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moduli Spaces of Hyperplanar Admissible Flags in Projective Space Cooper, George Algebraic Geometry 14D20, 14D22 We prove the existence of quasi-projective coarse moduli spaces parametrising certain complete flags of subschemes of a fixed projective space $\mathbb{P}(V)$ up to projective automorphisms. The flags of subschemes being parametrised are obtained by intersecting non-degenerate subvarieties of $\mathbb{P}(V)$ of dimension $n$ by flags of linear subspaces of $\mathbb{P}(V)$ of length $n$, with each positive dimension component of the flags being required to be non-singular and non-degenerate, and with the dimension $0$ components being required to satisfy a Chow stability condition. These moduli spaces are constructed using non-reductive Geometric Invariant Theory for actions of groups whose unipotent radical is graded, making use of a non-reductive analogue of quotienting-in-stages developed by Hoskins and Jackson. |
| title | Moduli Spaces of Hyperplanar Admissible Flags in Projective Space |
| topic | Algebraic Geometry 14D20, 14D22 |
| url | https://arxiv.org/abs/2304.02453 |