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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[AHH]AHH A. Aramova, J. Herzog, and T. Hibi: Gotzmann theorems for exterior algebras and combinatorics J. Algebra 191 (1997), 174–211.
[Ei]Ei D. Eisenbud: Commutative Algebra with a View Towards Algebraic Geometry, Springer Verlag, New York 1995.
[EFS]EFS D. Eisenbud, G. Fløystad, and F.-O. Schreyer: Sheaf cohomology and free resolutions over exterior algebras, Trans. Amer. Math. Soc. 355 (2003) 4397–4426.
[ESW]ESW D. Eisenbud, F.-O. Schreyer, and J. Weyman: Resultants and Chow forms via Exterior Syzygies, J. Amer. Math. Soc. 16 (2003) 537–579.
[EK]EK S. Eliahou and M. Kervaire: Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), 1–25.
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[Mac]Mac D. Maclagan: Antichains of monomial ideals are finite, Proc. Amer. Math. Soc. 129 (2001), 1609–1615.
[Pa]Pa K. Pardue: Deformation classes of graded modules and maximal Betti numbers, Ill. J. Math. 40 (1996), 564–585.
Additional Information
Irena Peeva
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853
MR Author ID:
263618
Email:
irena@math.cornell.edu
Mike Stillman
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14853
MR Author ID:
167420
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
