The Red Book of Varieties and Schemes Second, Expanded Edition. Incl
Mumford's famous Red Book gives a simple readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduate students or mat
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Lecture Notes in Mathematics Editors: A. Dold. Heidelberg F. Takens, Gro ningcn B. Teissier. Paris
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Springer Berlin Heidelberg New York Barcelona Hong Kong London. Milan Paris
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David Mumford
The Red Book of Varieties and Schemes Second, Expanded Edition Includes the Michigan Lectures (1974) on Curves and their Jacobians
Springer
Auth or s David B. Mumford
Division of Applied Mathematics, Box F Brown Unive rsity
Providence. RI 02912. USA E-mail: David_Mumford @brown.edu Enrico Arb are llo Scuo la Normale Superiore 7, Piazza dei Cava lieri 56 126 Pisa, Italy Ecmui l: ea@ bibsns.s ns.it
C utalog ing- in-Public atlon Data applied for
Die Deutsche Bibliothek - C [P-Einhcitsaufna hme
Mumford, David : TIle red boo k of va riet ies and sc he mes : includes the Mi chig an lectures (1974) on curves and the ir Jacobian s I David Mumford. - 2., expande d ed. - Berli n ; Heidelbe rg ; New York ; Barcel on a ; Hong Ko ng; Lo ndo n; M ilan; Pari s ; Sin ga po re ; Tok yo: Springer, 1999 (Lecture Dotes in mathema tics ; [358) ISBN 3-540-63293-X Mathematics Subject Classific ation ( 199 1): 14-0 1. 14A15. 14H10. 14H42. 14II 45
ISSN 0075- 8434 ISBN 3-540-63293-X Springer-Ve rlag Berlin Heidelberg New York Thi s work is subjec t to copy right. A ll right s arc reser ved, whether the whole or part of the material is co ncerned. speci fically the rights of tra nslation . reprinting. re-use of illustrations, recitation. broa dcasti ng. reproduction o n microfi lms or in an y ot her way. and storage in data ba nks. Dupl ication of this pub lication or pans thereof is permitted only under the provis ions of the Ge rman Co pyrig ht Law of Septe mber 9. 1965. in its cu rrent vers ion, and permiss ion for use must always be obtained from Sp ringe r-Verl ag. Viol ation s are liable for prosecuti on under the German Co pyright Law. © Springe r-Verlag Berlin Heidelberg 1999 Print ed in Germany Th e use of genera l descr iptiv e names, reg istered nam es. trade mark s, etc. in this pub lica tion does not imp ly, even in the absence of a specific statement, that such names arc exe mpt from the relevant protective laws and regulation s and therefore frce for ge nera l use. Typesetting: 1. Jebram using a Springe r-TpX macro-package
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Preface to the Second Edition
At t he sa me t ime that the first edition of t he Springer Lectu re Not es version of t he "Red Book of Varieties and Schemes" was sold out , th e supp ly of my lecture not es "Curves a nd their J acobians" , published by t he University of Michigan Pr ess, was also exhausted an d t he copyright retu rned to me. T hese two sets of not es have similar purposes. At one ti me, I had had a mbit ious plan s to write a multi-volum e introduction to algebraic geometry and specifically to moduli prob lems, this being t he par t of the field which I knew best . Before writ ing these, I gave lectures on various oc casions to explain the ideas informally with
t he idea t hat t hese might be a f
