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2015 Schubert decompositions for quiver Grassmannians of tree modules
Oliver Lorscheid
Algebra Number Theory 9(6): 1337-1362 (2015). DOI: 10.2140/ant.2015.9.1337


Let Q be a quiver, M a representation of Q with an ordered basis and e¯ a dimension vector for Q. In this note we extend the methods of Lorscheid (2014) to establish Schubert decompositions of quiver Grassmannians Gre¯(M) into affine spaces to the ramified case, i.e., the canonical morphism F : T Q from the coefficient quiver T of M w.r.t.  is not necessarily unramified.

In particular, we determine the Euler characteristic of Gre¯(M) as the number of extremal successor closed subsets of T0, which extends the results of Cerulli Irelli (2011) and Haupt (2012) (under certain additional assumptions on ).


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Oliver Lorscheid. "Schubert decompositions for quiver Grassmannians of tree modules." Algebra Number Theory 9 (6) 1337 - 1362, 2015.


Received: 22 August 2013; Revised: 23 February 2015; Accepted: 17 June 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1366.14044
MathSciNet: MR3397404
Digital Object Identifier: 10.2140/ant.2015.9.1337

Primary: 14M15
Secondary: 05C05 , 16G20

Keywords: Euler characteristics , quiver grassmannian , Schubert decompositions , tree modules

Rights: Copyright © 2015 Mathematical Sciences Publishers


Vol.9 • No. 6 • 2015
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