Minimal Free Resolutions of Fiber Products

Hugh Geller

Minimal Free Resolutions of Fiber Products

Commutative Algebra 2021-04-12 v1

Authors: Hugh Geller

Abstract

We construct free resolutions for quotient rings $R/\langle \mathcal{I}', \mathcal{I}\mathcal{J}, \mathcal{J}'\rangle$ , give conditions for the quotient to be realized as a fiber product, and give criteria for the construction to be minimal. We then specialize this result to fiber products over a field $k$ and recover explicit formulas for Betti numbers, graded Betti numbers, and Poincar\'{e} series.

Keywords

minimal free resolution fiber product quotient ring betti numbers graded betti numbers poincaré series commutative algebra

Cite

@article{arxiv.2104.04390,
  title  = {Minimal Free Resolutions of Fiber Products},
  author = {Hugh Geller},
  journal= {arXiv preprint arXiv:2104.04390},
  year   = {2021}
}

Comments

14 pages

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