PreprintCC BY 4.0HAL
Degenerations of Chain Complexes
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.
Related
- Varieties of chain complexes and mixed dimer covers
- Discriminants of Hermitian forms, maximal degenerations and Kontsevich's tropical approach to the Hodge conjecture
- Hodge Theory and Grobner Degenerations
- Ampleness of non-symmetric line bundles on degenerations of abelian varieties
- Monge-Ampère degenerations and conifold contractions in Fujiki class 𝒞
BibTeX
@misc{marquardt2026degenerations,
title = {{Degenerations of Chain Complexes}},
author = {Judith Marquardt},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28051},
eprint = {2609.28051},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05762268v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Degenerations of Chain Complexes
AU - Judith Marquardt
PY - 2026
DA - 2026/09/23
PB - HAL
DO - 10.48550/arxiv.2609.28051
UR - https://hal.science/hal-05762268v1
AB - 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.
ER -