2021/04/09 by Hugh Geller, Geller, Hugh · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 13D02 #secondary 13D07
paper · pdf · doi:10.48550/arxiv.2104.04390
openalex publication_date 2021/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct free resolutions for quotient rings R/⟨ I', IJ, J'⟩, 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 Poincaré series.