L. Szpiro's conjecture on Gorenstein algebras in codimension 2

Details L. Szpiro's conjecture on Gorenstein algebras in codimension 2 L. Szpiro's conjecture on Gorenstein algebras in codimension 2

2004-02-23

arxiv.org/abs/math/0402370v1

Mathematics

Commutative Algebra

20 pages

Scientific paper

A Gorenstein A-algebra R of codimension 2 is a perfect finite A-algebra such that R=Ext^2(R,A) holds as R-modules, A being a Cohen-Macaulay local ring with dim(A)-dim_A(R)=2. I prove a structure theorem for these algebras improving on an old theorem of M. Grassi. Special attention is paid to the question how the ring structure of R is encoded in its Hilbert resolution. It is shown that R is automatically a ring once one imposes a weak depth condition on a determinantal ideal derived from a presentation matrix of R over A. The interplay of Gorenstein algebras and Koszul modules as introduced by M. Grassi is clarified. Questions of applicability to canonical surfaces in P^4 have served as a guideline in these investigations.

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