Moduli Spaces of Hyperplanar Admissible Flags in Projective Space
| Autor: | Cooper, George |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Summary of changes in current version: corrected certain technical lemmas, improved exposition and introduction, addition of a section discussing similar possible constructions |
| Databáze: | arXiv |
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