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Web page: Alexandru I. Suciu | Created: January 9, 2002 |
| Maintained by: Misha Kogan | URL: http://www.math.neu.edu/~GASC/gas/anderson.html |
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| Some families of Gorenstein algebras of height four, and Hilbert schemes of curves on P³ |
| Abstract: Gorenstein Artinian (GA) algebras
of given Hilbert function and socle degree j, quotients of a polynomial
ring R in r-variables, may be parametrized as a locally closed subvariety
of the projective space P(Rj) of degree-j forms in r up to k*
multiple.
We ask: Are the families PGor(H) of GA algebras of fixed Hilbert
function H irreducible? What is the closure of PGor(H) in
P(Rj)?
We begin by answering these questions for complete interesections in two variables where there is a connection to determinantal ideals of Hankel matrices. This problem is also well understood in three variables, due to work of S.J. Diesel, J.-O. Kleppe, M. Boij, and others, based on the Buchsbaum-Eisenbud Pfaffian structure theorem for height three Gorenstein ideals. I will give an overview of work joint with Hema Srinivasan, on certain families for r=4, where H=Hh=(1,4,7,h,7,4,1), 7< h< 11. When h=8,9 the components of PGor(H) are closely related to components of certain Hilbert schemes of curves in P³. Which sequences H may occur is known for r=2,3,
but not for r=4. We show
The proofs use properties of minimal resolutions, the Hilbert schemes
of curves in P³, the smoothness of
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Web page: Alexandru I. Suciu | Created: January 9, 2002 |
| Maintained by: Misha Kogan | URL: http://www.math.neu.edu/~GASC/gas/anderson.html |