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arXiv · 2104.04390

Minimal Free Resolutions of Fiber Products

Hugh Geller
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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.

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Hugh Geller. 2021-04-09. Minimal Free Resolutions of Fiber Products. https://arxiv.org/abs/2104.04390

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