射影空间中超平面型可容许旗的模空间
Moduli Spaces of Hyperplanar Admissible Flags in Projective Space
AI总结：
该研究证明了射影空间中满足特定非退化、非奇异与周炜良稳定性条件的超平面型可容许旗的拟射影粗模空间存在性，并借助非约化几何不变量理论及分阶段取商的非约化类似方法完成构造。
摘要：
我们证明了拟射影粗模空间的存在性，这类空间用于参数化固定射影空间$\boldsymbol{\rm P}(V)$中某些完整子概型旗在射影自同构下的等价类。被参数化的子概型旗由$\boldsymbol{\rm P}(V)$中$n$维非退化子簇与$\boldsymbol{\rm P}(V)$中长度为$n$的线性子空间旗相交得到，要求旗的所有正维分量均非奇异且非退化，0维分量需满足周炜良稳定性条件。这些模空间通过针对单幂根基为分次的群作用的非约化几何不变量理论构造，用到了Hoskins与Jackson提出的分阶段取商的非约化类似方法。
英文摘要：
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.
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