Degeneration of A-infinity modules

TL;DR

This paper explores the use of A-infinity modules to analyze the derived category of finite-dimensional algebras, focusing on the geometric structure of parameterizing varieties and their orbit closures.

Contribution

It generalizes the description of orbit closures from modules to A-infinity modules, providing new insights into derived categories and their geometric parametrizations.

Findings

Orbit closures are characterized in A-infinity module varieties.

The work extends known results from module theory to A-infinity modules.

Provides a geometric framework for understanding derived categories.

Abstract

In this paper we use A-infinity modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A-infinity 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.