Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Connectedness of Hilbert schemes

Authors: Irena Peeva and Mike Stillman
Journal: J. Algebraic Geom. 14 (2005), 193-211
Published electronically: October 26, 2004
MathSciNet review: 2123227
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Abstract | References | Additional Information

Abstract: We show that the Hilbert scheme, that parametrizes all ideals with the same Hilbert function over an exterior algebra, is connected. We give a new proof of Hartshorne's Theorem that the classical Hilbert scheme is connected. More precisely: if $Q$ is either a polynomial ring or an exterior algebra, we prove that every two strongly stable ideals in $Q$ with the same Hilbert function are connected by a sequence of binomial Gröbner deformations.

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Additional Information

Irena Peeva
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853

Mike Stillman
Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853

Received by editor(s): March 26, 2003
Received by editor(s) in revised form: January 4, 2004
Published electronically: October 26, 2004
Additional Notes: Both authors are partially supported by the NSF

American Mathematical Society