Selected Papers II, 1st ed. 2010
On Algebraic Geometry, Including Correspondence with Grothendieck
Springer Collected Works in Mathematics Series

Author:

Language: English

84.39 €

In Print (Delivery period: 15 days).

Add to cartAdd to cart
Publication date:
767 p. · 15.5x23.5 cm · Paperback

These more than 30 articles span the years from 1961-1980 while David Mumford was an active researcher in the area of algebraic geometry. While Volume I contained the papers on classification of varieties and moduli spaces, Volume II contains all other papers in algebraic geomtetry, such as Mumford's paper with Pierre Deligne, The Irreducibility of the space of curves of given genus (1969). Mumford's correspondence of the years 1958 to 1986 with Alexander Grothendieck is also included.

From the reviews of Volume II:

?Selected Papers Volume II collects twenty-nine articles by Mumford, along with four previously unpublished pieces and dozens of letters between Mumford and Grothendieck. ? this book the same way I felt about the first volume: this is a book that most algebraic geometers ? and all libraries ? will not want to do without.? (Darren Glass, The Mathematical Association of America, October, 2010)

Preface.- Topology of normal singularities and a criterion for simplicity.- The canononical ring of an algebraic surface.- Some aspects of the problem of moduli.- Two fundamental theorems on deformations of polarized varieties.- A remark on Mordell's conjecture.- Picard groups of moduli problems.- Abelian quotients of the Teichmuller modular group.- Deformations and liftings of finite, commutative group schemes.- Bi-extentions of formal groups.- The irreducibility of the space of curves of given genus.- Varieties defined by quadratric equations, with an appendix by G. Kempf.- A remark on Mahler's compactness theorem.- Introduction to the theory of moduli.- An example of a unirational 3-fold which is not rational.- A remark on the paper of M. Schlessinger.- Matsusaka's big theorem.- The self-intersection formula and the 'forumle-clef'.- Hilbert's fourteenth problem-the finite generation of subrings such as rings of invariants.- The projectivity of the moduli space of stable curves. I. Preliminaries on 'det' and 'Div'.- An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related nonlinear equation.- The work of C.P. Ramanujam in algebraic geometry.- Some footnotes to the work of C.P. Ramanujam.- Fields medals. IV. An instinct for the key idea.- The spectrum of difference operators and algebraic curves.- Proof of the convexity theorem.- Oscar Zariski: 1899-1986.- Foreward for non-mathematicians.- What can be computed in algebraic geometry.- In memoriam: George R. Kempf 1944-2002.- Boundary points on modular varieties.- Further comments on boundary points.- Abstract theta functions.- Abstract theta functions over local fields.

David Mumford was Professor of Applied Mathematics at Brown University.  In 1974 he was awarded the Fields Medal at the International Congress of Mathematicians in Vancouver.

Includes many important papers which were not published in volume I, including his paper with Deligne from 1969 Many of these papers are no longer available elsewhere Includes correspondence between Mumford and Grothendieck, arguably the most important figure in 20th century algebraic geometry