Connected sums of Gorenstein local rings
-
H. Ananthnarayan
,
Luchezar L. Avramov
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 sumR⋕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.
©[2012] by Walter de Gruyter Berlin Boston
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- Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities
- Almost prime Pythagorean triples in thin orbits
- Hessian inequalities and the fractional Laplacian
- Connected sums of Gorenstein local rings
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Articles in the same Issue
- Diffusion determines the manifold
- Semicomplete meromorphic vector fields on complex surfaces
- Zeroth Poisson homology of symmetric powers of isolated quasihomogeneous surface singularities
- Almost prime Pythagorean triples in thin orbits
- Hessian inequalities and the fractional Laplacian
- Connected sums of Gorenstein local rings
- The restricted Weyl group of the Cuntz algebra and shift endomorphisms
- Braided cofree Hopf algebras and quantum multi-brace algebras
- Static Klein–Gordon–Maxwell–Proca systems in 4-dimensional closed manifolds
