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arXiv · 1401.5028

Orbit closures and rational surfaces

Frauke M. Bleher·Ted Chinburg·Birge Huisgen-Zimmermann
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Abstract

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.

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BibTeXRIS

Frauke M. Bleher, Ted Chinburg, Birge Huisgen-Zimmermann. 2014-01-20. Orbit closures and rational surfaces. https://doi.org/10.1016/j.jpaa.2015.10.002

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