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Abstract:
Let B be a graded Cohen-Macaulay (CM) quotient of a polynomial ring R.
If K, the canonical module of B, is locally free in some open set, one
knows that a regular section f of the twisted B-dual K*(s) defines a
Gorenstein quotient A given by
(1) A = B/im f.
More generally if M is
a (locally free) maximal CM module of rank < 4 whose top exterior power
is locally a twist of K, then again a regular section of M*(s) defines
a Gorenstein algebra by (1).
Let GradAlg(H) be the scheme (similar to the usual Hilbert scheme)
parametrizing graded quotients of R with fixed Hilbert function H, and
let W be the subset of points (A) constructed by (1), by varying B, f
and M. In the talk we examine the unobstructedness of A, the dimension
of W and we look to whether W is dense in GradAlg(H) or not, with a
special focus to Gorenstein algebras of codimension 4 of R.
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