Moduli Spaces of Hyperplanar Admissible Flags in Projective Space

2023/04/05 by Cooper, George
#14D20 #14D22 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.02453

Abstract

We prove the existence of quasi-projective coarse moduli spaces parametrising certain complete flags of subschemes of a fixed projective space ℙ(V) up to projective automorphisms. The flags of subschemes being parametrised are obtained by intersecting non-degenerate subvarieties of ℙ(V) of dimension n by flags of linear subspaces of 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.

Related

• Projective completions of graded unipotent quotients
• Spaces of quasi-maps into the flag varieties and their applications
• Quotients by non-reductive algebraic group actions
• Stratifying quotient stacks and moduli stacks
• Existence of affine pavings for varieties of partial flags associated to\n nilpotent elements