Connected sums of Gorenstein local rings

By H. Ananthnarayan, L. Avramov, W. F. Moore. 2010

60 citations recorded by the source corpus.

Abstract Given surjective homomorphisms R → T ← S of local rings, and ideals in R and S that are isomorphic to some T-module V, the connected sum R⋕TS is defined to be the ring obtained by factoring out the diagonal image of V in the fiber product R ×TS. When T is Cohen–Macaulay of dimension d and V is a canonical module of T, it is proved that if R and S are Gorenstein of dimension d, then so is R⋕TS. This result is used to study how closely an artinian ring can be approximated by a Gorenstein ring mapping onto it. When T is regular, it is shown that R⋕TS almost never is a complete intersection ring. The proof uses a presentation of the cohomology algebra as an amalgam of the algebras and over isomorphic polynomial subalgebras generated by one element of degree 2.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6495884dbef93cecaeee4b06d7d13840e576aab4

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In Algebra and Number Theory

1. C. Finocchiaro
2. Marco Fontana
3. Marco D'anna

In Geometry and Topology

1. Marco Fontana
2. C. Finocchiaro
3. Marco D'anna

Citations in the corpus

• New Algebraic Properties of an Amalgamated Algebra Along an Ideal (2016, background): “In [1] the authors consider a new construction, called connected sum of local rings, obtained by taking a quotient of a pullback for which both homomorphisms and are surjective.”