A constructive approach to one-dimensional Gorenstein k-algebras

Abstract: Codimension three Gorenstein rings are completely described by Buchsbaum and Eisenbud's structure theorem, but despite many attempts the construction of Gorenstein rings is an open problem in higher codimension. Gorenstein rings are of great interest in many areas of mathematics and they have appeared as an important component in a significant number of problems. Our task is to give a procedure for constructing all $1$-dimensional Gorenstein $k$-algebras. Applications to the Gorenstein linkage of zero-dimensional schemes and to Gorenstein affine semigroup rings are discussed. The results are based on recent results obtained jointly with J. Elias.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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