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Orbit closures and rational surfaces
Journal article   Open access   Peer reviewed

Orbit closures and rational surfaces

Frauke M Bleher, Ted Chinburg and Birge Huisgen-Zimmermann
Journal of pure and applied algebra, Vol.220(5), pp.1785-1812
01/20/2014
DOI: 10.1016/j.jpaa.2015.10.002

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Abstract

J. Pure Appl. Algebra 220 (2016), 1785-1812 In this paper we study the Grassmannian of submodules of a given dimension inside a finitely generated projective module $P$ for a finite dimensional algebra $\Lambda$ over an algebraically closed field. The orbit of such a submodule $C$ under the action of $\mathrm{Aut}_\Lambda ( P )$ on the Grassmannian encodes information on the degenerations of $P/C$ and has been considered by a number of authors. The goal of this article is to bound the geometry of two-dimensional orbit closures in terms of representation-theoretic data. Several examples are given to illustrate the interplay between the geometry of the projective surfaces which arise and the corresponding posets of degenerations.
Mathematics - Representation Theory

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