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
DOI: https://doi.org/10.1090/S1056-3911-04-00386-8
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
Email: irena@math.cornell.edu

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

DOI: https://doi.org/10.1090/S1056-3911-04-00386-8
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

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
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