Obstructions to deforming a space curve

Author:
Daniel J. Curtin

Journal:
Trans. Amer. Math. Soc. **267** (1981), 83-94

MSC:
Primary 14D15

MathSciNet review:
621974

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Abstract: Mumford described a curve, , in that has obstructed infinitesimal deformations (in fact the Hilbert scheme of the curve is generically nonreduced). This paper studies Hilbert scheme by studying deformations of in over parameter spaces of the form . Given a deformation of over one attempts to extend it to a deformation of over . If it will not extend, this deformation is said to be *obstructed at the nth order*.

I show that on a generic version of Mumford's curve, an infinitesimal deformation (i.e., a deformation over ) is either obstructed at the second order, or at no order, in which case we say it is *unobstructed*.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1981-0621974-2

Keywords:
Projective space curves,
infinitesimal deformations,
obstructed deformations,
deformations of cones,
Hilbert scheme

Article copyright:
© Copyright 1981
American Mathematical Society