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Mathematics - Algebra | Selected Papers - Volume II: On Algebraic Geometry, including Correspondence with Grothendieck

Selected Papers

Volume II: On Algebraic Geometry, including Correspondence with Grothendieck

Volume package: Selected Papers

Mumford, David

Neeman, Amnon, Chai, Ching-Li, Shiota, Takahiro (Eds.)

2010, XXII, 767 p.

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ISBN 978-0-387-72491-1

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ISBN 978-1-4899-9174-4

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  • 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

From the reviews of Volume I:

"I am quite happy to keep this volume on my shelf, and I will surely find many more seeds in it that grew so large that by now their origins are hard to recognize." Janos Kollar, Bulletin of the AMS.

"... 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..."

Werner Kleinert, Zentralblatt MATH.

These 30+ articles span the years from 1961-1980 while David Mumford was an active researcher in the area of algebraic geometry. While Volume I was very successful, there were papers which were left out, and will now be included here, such as Mumford's paper with Pierre Deligne, The Irreducibility of the space of curves of given genus (1969). Mumford's correspondence with Grothendieck will also be included.

Content Level » Research

Related subjects » Algebra - Number Theory and Discrete Mathematics

Table of contents 

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.

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