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Connectedness of Hilbert schemes
Author(s):
Irena
Peeva;
Mike
Stillman
Journal:
J. Algebraic Geom.
14
(2005),
193-211.
Posted:
October 26, 2004
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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  is either a polynomial ring or an exterior algebra, we prove that every two strongly stable ideals in  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
PII:
S 1056-3911(04)00386-8
Received by editor(s):
March 26, 2003
Received by editor(s) in revised form:
January 4, 2004
Posted:
October 26, 2004
Additional Notes:
Both authors are partially supported by the NSF
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