Degenerations of chain complexesOberseminar Algebra und Darstellungstheorie

by Judith Marquardt (Université Grenoble Alpes)

Thursday Jul 23, 2026, 5:00 PM → 6:00 PM Europe/Berlin

Endenicher Allee 60/1-008 - Seminarraum (Mathezentrum)

Riedtmann and Zwara have characterized degenerations of orbits in module varieties in terms of certain short exact sequences.  In this talk, 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. 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 using distinguished triangles in the category. This links to an algebraic definition of degeneration for triangulated categories introduced by Jensen, Su and Zimmermann.