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Inequidimensionality of Hilbert schemes

Author(s): Mei-Chu Chang
Journal: Proc. Amer. Math. Soc. 125 (1997), 2521-2526.
MSC (1991): Primary 14J29; Secondary 14M07, 14M12
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Abstract: We give a lower bound on the number of distinct dimensions of irreducible components of the Hilbert scheme of codimension 2 subvarieties in $\mathbb {P}^{n}$, for $n \le 5$ (respectively, the moduli space of surfaces or 3-folds) in terms of the Hilbert polynomial (resp. Chern numbers).

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Additional Information:

Mei-Chu Chang
Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, University of California, Riverside, California 92521
Email: mcc@math.ias.edu, mcc@math.ucr.edu

DOI: 10.1090/S0002-9939-97-03836-7
PII: S 0002-9939(97)03836-7
Keywords: Hilbert scheme, moduli space, projectively normal subvarieties, deformation theory, dimension
Received by editor(s): October 5, 1995
Received by editor(s) in revised form: March 14, 1996
Additional Notes: The author was partially supported by NSF Grant No. DMS 9304580.
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 1997, American Mathematical Society

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