Titel: Deformations of Algebraic Schemes
Autor/en: Edoardo Sernesi
'Grundlehren der mathematischen Wissenschaften'.
Springer Berlin Heidelberg
6. Juli 2006 - gebunden - 356 Seiten
The study of small and local deformations of algebraic varieties originates in the classical work of Kodaira and Spencer and its formalization by Grothendieck in the late 1950's. It has become increasingly important in algebraic geometry in every context where variational phenomena come into play, and in classification theory. Today deformation theory is highly formalized and has ramified widely. This self-contained account of deformation theory in classical algebraic geometry (over an algebraically closed field) brings together for the first time some results previously scattered in the literature, with relatively little known proofs, yet of everyday relevance to algebraic geometers. It also includes applications to the construction and properties of Severi varieties of families of plane nodal curves, space curves, deformations of quotient singularities, Hilbert schemes of points, local Picard functors, etc. The exposition, amenable at graduate student level, includes many examples.
Infinitesimal deformations.- Formal deformation theory.- Examples of deformation functors.- Hilbert and Quot schemes.
Edoardo Sernesi - vita
Present position:Professore ordinario di Geometria, FacoltÃ di Scienze MFN, UniversitÃ Roma Tre
Education:- Laurea in Matematica- UniversitÃ di Roma, 1969 - Ph.D. in Mathematics - Brandeis University, 1976
Professional experience:- Assistente ordinario di Geometria, UniversitÃ di Ferrara, 1974-1980.- Professore straordinario di Geometria UniversitÃ di Roma ``La Sapienza", 1980-1983.- Professore ordinario di Geometria UniversitÃ di Roma ``La Sapienza", 1983-1992.- Professore ordinario di Geometria UniversitÃ Roma Tre, from 1992.
From the reviews:
"One of the goals of Springer's Grundlehren series is to provide reliable and thorough accounts of certain portions of mathematics. This volume by Edoardo Sernesi does just that, and hence fits the series well. ... So this is a book for algebraic geometers; for them, it'll prove to be a useful resource and reference." (Fernando Q. Gouvêa, MathDL, August, 2006)
"Without any doubt, this is a masterly book on a highly advanced topic in algebraic geometry. ... The entire text is kept at a level that makes it suitable for graduate students ... . But even for experts and active researchers in algebraic geometry, this unique book on algebraic deformation theory offers a great deal of inspiration and new insights, too, and its future role as a standard source and reference book in the field can surely be taken for granted from now on." (Werner Kleinert, Zentralblatt MATH, Vol. 1102 (4), 2007)
"The book under review gives an introduction to classical deformation theory using modern language, and is apparently unique among textbooks in the recent literature in that it is largely self-contained and covers the main topics ... . It will be attractive for graduate students with a basic knowledge of commutative algebra and algebraic geometry as a base for advanced lectures. The need for such a book was evident for a long time; the reviewer is happy to have it on his bookshelf." (Marko Roczen, Mathematical Reviews, Issue 2008 e)