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Extension-orthogonal components of nilpotent varieties

Christof Geiß·Jan Schröer
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Abstract

Let Q be a Dynkin quiver, and let P(Q) be the corresponding preprojective algebra. Let I be a set of pairwise different indecomposable irreducible components of varieties of P(Q)-modules such that generically there are no extensions between these components. We show that the number of elements in I is at most the number of positive roots of Q. Furthermore, we give a module theoretic interpretation of Leclerc's counterexample to a conjecture of Berenstein and Zelevinsky.

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Christof Geiß, Jan Schröer. 2002-08-27. Extension-orthogonal components of nilpotent varieties. https://doi.org/10.1090/s0002-9947-04-03555-x

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