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Selected Papers : On the Classification of Varieties and Moduli Spaces - David Mumford

Selected Papers

On the Classification of Varieties and Moduli Spaces


Published: 15th July 2004
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These 30 articles span the years from 1961-1980 while David Mumford was an active researcher in the area of algebraic geometry. In addition, each of the three sections is introduced with never before published commentary by David Gieseker, Eckart Viehweg, and George Kempf and Herbert Lange.

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)

"Springer has recently released ... a collection of 30 of the 51 papers that Mumford wrote in algebraic geometry. The papers are divided into three sections, each of which comes with commentary and annotation by Mumford ... which give nice summaries and introductions to much of his work. ... Reading these papers is exciting both for their mathematical content and to watch the evolution of the ideas ... . a book that most algebraic geometers - and all libraries - will not want to do without." (Darren Glass, MathDL, January, 2005)

"The Editors of this volume of Selected Papers, published by Springer Verlag, have made the choice of grouping his articles under three distinct headings ... . This is a book is not going to get dust on a shelf: it will more likely spend its life on desks, read more often than a Graduate Text or a Monograph. Algebraic geometers of every generation will certainly welcome it." (E. Sernesi, Jahresbericht der Deutschen Mathematiker-Vereinigung, Vol. 107 (1), 2007)

"This book contains a selection of the papers of David Mumford (born in 1937) in algebraic geometry. Even today, his papers are a rich source of information, of truly new ideas, and of inspiration. ... His style is unique and fascinating. ... Young algebraic geometers would do well to study these papers. They contain a wealth of ideas waiting to be developed." (Frans Oort, Nieuw Archief voor Wiskunde, Vol. 8 (3), 2007)

"I am quiet happy to keep this volume on my self, and I will surely find many more seeds in it that grew so large that by now there origins are hard to recognize. The volume under review divides Mumford's papers into three broad areas, each preceded by an easy summarizing the results and outlining their influence on further developments." (Janos Kollar, Bulletin of the American Math Society, Vol. 43 (1), 2005)

Geometric invariant theory and the moduli of curves
Commentaryp. 1
An elementary theorem in geometric invariant theory (1961)p. 18
Projective invariants of projective structures and applications (1962)p. 23
Periods of a moduli space of bundles on curves (1968)p. 28
The structure of the moduli spaces of curves and abelian varieties (1970)p. 37
An analytic construction of degenerating curves over complete local rings (1972)p. 46
Pathologies IV (1975)p. 92
Stability of projective varieties (1977)p. 95
On the Kodaira dimension of the moduli space of curves (1982)p. 171
Towards an enumerative geometry of the moduli space of curves (1983)p. 235
Theta functions and the moduli of abelian varieties
Commentaryp. 293
On the equations defining abelian varieties : I (1966)p. 309
On the equations defining abelian varieties : II (1967)p. 377
On the equations defining abelian varieties : III (1967)p. 438
Families of abelian varieties (1966)p. 468
A note on Shimura's paper "Discontinuous groups and abelian varieties" (1969)p. 473
Theta characteristics of an algebraic curve (1971)p. 480
An analytic construction of degenerating abelian varieties over complete rings (1972)p. 492
A rank 2 vector bundle of P[superscript 4] with 15,000 symmetries (1973)p. 526
Prym varieties (1974)p. 545
A new approach to compactifying locally symmetric varieties (1973)p. 571
Hirzebruch's proportionality theorem in the non-compact case (1977)p. 585
On the Kodaira dimension of the Siegel modular variety (1983)p. 619
The classification of surfaces and other varieties
Commentaryp. 647
Enriques' classification of surfaces in char p : I (1969)p. 660
Enriques' classification of surfaces in char p : II (1979)p. 675
Enriques' classification of surfaces in char p : III (1976)p. 695
Pathologies of modular algebraic surfaces (1961)p. 731
Further pathologies in algebraic geometry (1962)p. 735
Pathologies III (1967)p. 743
Rational equivalence of 0-cycles on surfaces (1969)p. 753
Some elementary examples of unirational varieties which are not rational (1972)p. 763
An algebraic surface with K ample, (K[superscript 2]) = 9, p[subscript g] = q = 0 (1979)p. 784
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387210926
ISBN-10: 038721092X
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 795
Published: 15th July 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.5 x 15.5  x 4.45
Weight (kg): 1.49