Year: 2024
Type: article
Abstract: The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction having the same name. We determine the graded Betti numbers for connected sums of graded Artinian Gorenstein algebras. Along the way, we find the graded Betti numbers for fiber products of graded rings; an analogous result was obtained in the local case by Geller [Proc. Amer. Math. Soc. 150 (2022), pp. 4159–4172]. We relate the connected sum construction to the doubling construction, which also produces Gorenstein rings. Specifically, we show that, for any number of summands, a connected sum of doublings is the doubling of a fiber product ring.
DOI: 10.1090/tran/9286
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1411957492, Polynomial Interpolation, Symmetric Ideals, and Lefschetz Properties, G3565572578, G4771248631, G6379094992, Symbolic Powers and Lefschetz Properties: Geometric and Homological Aspects, G7376931544, Finite Group Actions on Free Resolutions, G8181116839, G8482122285, G8858688717, G8941627833
OpenAlex ID: W4403463596