Year: 2026
Type: preprint
Abstract: We study degenerations of orbits in varieties of chain complexes of projective modules. We show that degenerations are characterized in terms of certain admissible short exact sequences in the exact category of complexes of projectives, analogously to work from Riedtmann and Zwara. We then extend our study to the homotopy category. In this context, complexes of projectives with a given $g$-vector form an ind-variety, and we prove that degenerations of orbits are characterized by the existence of certain distinguished triangles in the category. This links to the algebraic definition of degeneration for triangulated categories introduced by Jensen, Su and Zimmermann.
Source: arXiv (Cornell University)
Author: Marquardt, Judith
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G553375094
OpenAlex ID: W7214195518