Lectures on deformations of singularities
Lectures on deformations of singularities by Michael. Seshadri, C. S. ; Tannenbaum, Allen, Artin
English | 1976 | ASIN: B007F7DZS0 | 110 Pages | PDF | 1 MB
English | 1976 | ASIN: B007F7DZS0 | 110 Pages | PDF | 1 MB
These notes are based on a series of lectures given at the Tata Institute in January-February, 1973. The lectures are centered about the work of M. Scahlessinger and R. Elkik on infinitesimal deformations. In general, let X be a flat scheme over a local Artin ring R with residue field k. Then one may regard X as an infinitesimal deformation of the closed fiber x0 = XSpe×c(R) Spec(k). Schlessinger’s main result proven in part (for more information see his Harvard Ph.D. thesis) is the construction, under certian hypotheses, of a “versal deforamtion space” for X0. He shows that ∃ a complete local k-algebra A = limA/mn A and a sequence of deformations Xn over Spec(A/mn A) such that the formal A-prescheme X = lim −−→ Xn is versal in this sense: For all Artin local rings R, every deformation S/S pec(R) of X0 may be obtained from some homomorphism A → R by setting X = X Spe×c(A) Spec(R).