Universität zu Köln

Irelli, Giovanni Cerulli, Fang, Xin, Feigin, Evgeny, Fourier, Ghislain and Reineke, Markus (2020). Linear degenerations of flag varieties: partial flags, defining equations, and group actions. Math. Z., 296 (1-2). S. 453 - 478. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1823

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Irelli, Giovanni Cerulli UNSPECIFIED UNSPECIFIED UNSPECIFIED Fang, Xin UNSPECIFIED UNSPECIFIED UNSPECIFIED Feigin, Evgeny UNSPECIFIED UNSPECIFIED UNSPECIFIED Fourier, Ghislain UNSPECIFIED UNSPECIFIED UNSPECIFIED Reineke, Markus UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-317825
DOI:	10.1007/s00209-019-02451-1
Journal or Publication Title:	Math. Z.
Volume:	296
Number:	1-2
Page Range:	S. 453 - 478
Date:	2020
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1823
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language QUIVER GRASSMANNIANS; MODULES; BASES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/31782