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PreprintCC BY-NC-ND 4.0arXiv

Pruning free resolutions over a complete intersection

  • Ben Betts
  • Janet Vassilev
Open at sourcePDFDOICite

Abstract

Given a free resolution F• over a polynomial ring R and a system of higher homotopies on it for a regular sequence a1,…,ac, we can use the Eisenbud-Shamash construction to build a free resolution over R̅=R/(a1,…,ac). We provide a combinatorial formula for the new system of higher homotopies on a pruned free resolution F•ℳ that corresponds to a pruning of the Eisenbud-Shamash resolution.

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Cite

BibTeXRIS
BibTeX
@misc{betts2026pruning,
  title = {{Pruning free resolutions over a complete intersection}},
  author = {Ben Betts and Janet Vassilev},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08764},
  eprint = {2611.08764},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08764},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Pruning free resolutions over a complete intersection
AU  - Ben Betts
AU  - Janet Vassilev
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08764
UR  - https://arxiv.org/abs/2611.08764
AB  - Given a free resolution F_• over a polynomial ring R and a system of higher homotopies on it for a regular sequence a_1,…,a_c, we can use the Eisenbud-Shamash construction to build a free resolution over R̅=R/(a_1,…,a_c). We provide a combinatorial formula for the new system of higher homotopies on a pruned free resolution F_•^ℳ that corresponds to a pruning of the Eisenbud-Shamash resolution.
ER  -