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Obstructions to Deforming a space curve

1981
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Transactions of the American Mathematical Society
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Mumford described a curve, y, in P3 that has obstructed infinitesimal deformations (in fact the Hubert scheme of the curve is generically nonreduced). This paper studies y's Hilbert scheme by studying deformations of y in P3 over parameter spaces of the form Spec(k[t]/(t")), n = 2, 3,. .. . Given a deformation of y over Spec(fc[f]/(f")) one attempts to extend it to a deformation of y over Spec(k[t]/(tn+ ')). If it will not extend, this deformation is said to be obstructed at the nth order, I

doi:10.2307/1998570
fatcat:td7u6sonv5b37ijk43f4bapqua