Selected Papers II

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.

• 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.

From the reviews:"The present volume contains thirty selected articles of D. Mumford on topics in algebraic geometry … . must be seen as a highly valuable and welcome collection for every researcher in the field. … Further generations of researchers in this field, graduate students, mathematical physicists, and mathematical historians will profit a great deal from this collection of selected papers … . this is why this volume is at least a must for any relevant library." (Werner Kleinert, Zentralblatt MATH, Vol. 1051)“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)“The present second volume of David Mumford’s paperson algebraic geometry, including his correspondence with Alexandre Grothendieck over a period of twenty-five years, must be seen as another hoard of Jewels from his treasury of mathematical writings. … this book contains a wealth of new information for the reader, and it is an utmost useful reference book moreover. … this book decidedly ought to be added to the private library of any algebraic geometer.” (Werner Kleinert, Zentralblatt MATH, Vol. 1211, 2011)