Obstructions to Deforming a space curve

Daniel J. Curtin
1981 Transactions of the American Mathematical Society  
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
more » ... the nth order, I show that on a generic version of Mumford's curve, an infinitesimal deformation (i.e., a deformation over Spec(k[t]/(t2))) is either obstructed at the second order, or at no order, in which case we say it is unobstructed.
doi:10.2307/1998570 fatcat:td7u6sonv5b37ijk43f4bapqua