Linear degenerations of flag varieties: partial flags, defining equations, and group actions

Giovanni Cerulli Irelli, Xin Fang*, Evgeny Feigin, Ghislain Fourier, Markus Reineke

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We continue, generalize and expand our study of linear degenerations of flag varieties from Cerulli Irelli et al. (Math Z 287(1–2):615–654, 2017). We realize partial flag varieties as quiver Grassmannians for equi-oriented type A quivers and construct linear degenerations by varying the corresponding quiver representation. We prove that there exists the deepest flat degeneration and the deepest flat irreducible degeneration: the former is the partial analogue of the mf-degenerate flag variety and the latter coincides with the partial PBW-degenerate flag variety. We compute the generating function of the number of orbits in the flat irreducible locus and study the natural family of line bundles on the degenerations from the flat irreducible locus. We also describe explicitly the reduced scheme structure on these degenerations and conjecture that similar results hold for the whole flat locus. Finally, we prove an analogue of the Borel–Weil theorem for the flat irreducible locus.

Original languageEnglish
Pages (from-to)453-477
Number of pages25
JournalMathematische Zeitschrift
Volume296
Issue number1-2
DOIs
StatePublished - 1 Oct 2020
Externally publishedYes

Funding

FundersFunder number
DFG-RSF
Russian Academic Excellence Project ?

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