Selected Papers: On the Classification of Varieties and Moduli Spaces

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Juli 2004



Mumford is a well-known mathematician and winner of the Fields Medal, the highest honor available in mathematics.
Many of these papers are currently unavailable, and the commentaries by Gieseker, Lange, Viehweg and Kempf are being published here for the first time.


Part I. Geometric Invariant Theory and the Moduli of Curves * Commentary by David Gieseker * An elementary theorem in geometric invariant theory (1961) * Projective invariants of projective structures and applications (1962) * Periods of a moduli space of bundles on curves (with P. Newstead) (1968) * The structure of the moduli spaces of curves and abelian varieties (1970) * An analytic construction of degenerating curves over complete local rings (1972) * Pathologies IV (1975) * Stability of projective varieties (1977) * On the Kodaira dimension of the moduli space of curves (with J. Harris) (1982) * Towards an enumerative geometry of the moduli space of curves (1983) * Part II. Theta Functions and the Moduli of Abelian Varieties * Commentary by George Kempf and Herbert Lange * On the equations defining abelian varieties. I (1966)* On the equations defining abelian varieties. II (1967) * On the equations defining abelian varieties. III (1967) * Families of abelian varieties (1966) * A note on Shimura's paper 'Discontinuous groups and abelian varieties' (1969) * Theta characteristics of an algebraic curve (1971) * An analytic construction of degenerating abelian varieties over complete rings (1972) * A rank 2 vector bundle of P^4 with 15,000 symmetries (with G. Horrocks) (1973) * Prym Varieties I (1974) * A new approach to compactifying locally symmetric varieties (1973) * Hirzebruch's Proportionality Theorem in the Non-Compact Case (1977) * On the Kodaira dimension of the Siegel modular variety (1983) * Part III. The Classification of Surfaces and Other Varieties * Commentary by Eckart Viehweg * Enriques' classification of surfaces in char p: I (1969) * Enriques' classification of surfaces in char p: II (with E. Bombieri) (1979) * Enriques' classification of surfaces in char p: III (with E. Bombieri) (1976) * Pathologies of modular algebraicsurfaces (1961) * Further pathologies in algebraic geometry (1962) * Pathologies III (1967) * Rational equivalence of 0-cycles on surfaces (1969) * Some elementary examples of unirational varieties which are not rational (with M. Artin) (1972) * An algebraic surface with K ample, (K^2) = 9, p_g = q = 0 (1979)




David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.§Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.


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." (János Kollár, Bulletin of the American Math Society, Vol. 43 (1), 2005)
EAN: 9780387210926
ISBN: 038721092X
Untertitel: On the Classification of Varieties and Moduli Spaces. 2004. Auflage. Sprache: Englisch.
Erscheinungsdatum: Juli 2004
Seitenanzahl: 795 Seiten
Format: gebunden
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