Lectures on deformations of singularities

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Lectures on deformations of singularities

مُساهمة من طرف aRET في الأحد يناير 14, 2018 6:38 pm




Lectures on deformations of singularities by Michael. Seshadri, C. S. ; Tannenbaum, Allen, Artin
English | 1976 | ASIN: B007F7DZS0 | 110 Pages | PDF | 1 MB
These notes are based on a series of lectures given at the Tata Institutein January-February, 1973. The lectures are centered about the work ofM. Scahlessinger and R. Elkik on infinitesimal deformations.

These notes are based on a series of lectures given at the Tata Institutein January-February, 1973. The lectures are centered about the work ofM. Scahlessinger and R. Elkik on infinitesimal deformations. In general,let X be a flat scheme over a local Artin ring R with residue fieldk. Then one may regard X as an infinitesimal deformation of the closedfiber 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. Heshows that ? a complete local k-algebra A = limA/mnA and a sequenceof deformations Xn over Spec(A/mnA) such that the formal A-preschemeX = lim??>Xn is versal in this sense: For all Artin local rings R, every deformationS/S pec(R) of X0 may be obtained from some homomorphismA > R by setting X = X Spe?c(A)Spec(R).
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