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Degeneration of A-infinity modules. (English) Zbl 1221.18009

Summary: We use \( A_{\infty}\)-modules to study the derived category of a finite-dimensional algebra over an algebraically closed field. We study varieties parameterising \( A_{\infty}\)-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Zwara and Riedtmann for modules.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
14L30 Group actions on varieties or schemes (quotients)
16G10 Representations of associative Artinian rings
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