The Collected Papers of Wei-Liang Chow

519 Pages·2002·28.26 MB·English

by  Wei-Liang Chow

THE COLLECTED PAPERS OF
WEI-LIANG CHOW
World Scientific Series in 20th Century Mathematics
Published
Vol. 1 The Neumann Compendium
edited by F. Brody and T. Vamos
Vol. 2 40 Years in Mathematical Physics
by L D. Faddeev
Vol. 3 Selected Papers of Yu I Manin
by Y. Manin
Vol. 4 A Mathematician and His Mathematical Work
— Selected Papers of S. S. Chern
edited by S. Y. Cheng, P. Li and G. Tian
Vol. 5 Fields Medallists' Lectures
edited by Sir Michael Atiyah and Daniel lagolnitzer
Vol. 6 Selected Logic Papers
by G. E. Sacks
Vol. 7 Selected Papers of F. W. J. Olver (in 2 Volumes)
edited by Roderick Wong
Vol. 8 The Collected Papers of Wei-Liang Chow
edited by S S Chern and V V Shokurov
World Scientific Series in 20th Century Mathematics Vol. 8
THE COLLECTED PAPERS OF
WEI-LIANG CHOW
Edited by
S. S. Chern
Nankai Institute of Mathematics, P. R. China
V. V. Shokurov
Johns Hopkins University, USA
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THE COLLECTED PAPERS OF WEI-LIANG CHOW
Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd.
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ISBN 981-238-094-9
Printed in Singapore by Mainland Press
WEI-LIANG CHOW
Courtesy of Margot Chow

Vll
PREFACE
This volume contains the collection of Chow's papers. It also includes:
• Chow's bibliography of all his publications in mathematics, except for,
his unpublished manuscript [Ch 55c] that is posted at
http://mathnt.mat.j hu.edu/mathnew/Chow/;
• Chow's biography in dates;
• Chern's remarks on Chow, previously published in the Notices of the
AMS;
• Lang's comments on Chow's work, a version previously published in
Contemporary Mathematics of the AMS; and
• an English translation by W. Huang of [1] (with wan der Waerden),
one of the most influential works by Chow.
The main part of this volume is presented by 34 published papers of Chow
in mathematics. After some of them we commented.
Acknowledgments: For partial support in preparation of this volume: the
Johns Hopkins University, Baltimore, the USA, and the Nankai Institute
of Mathematics, Tianjin, People's Republic of China. Picture courtesy of
Mrs. Chow. For typesetting and putting all materials in a right form thanks
to Carol Young and Mike Smith.
S. S. Chern and V. V. Shokurov*
"The second editor is supported in part by NSF grants DMS 9800807 and DMS
0100991.

IX
Biography
Wei-Liang Chow was born in Shanghai, China, on October 1, 1911. His
undergraduate and early graduate work were completed in the United States:
at Asbury College in Wilmore, Kentucky, at the University of Kentucky
(Lexington), and finally at the University of Chicago, where he received his
B.S. degree in 1931 and M.S. degree in 1932. Doctoral studies followed:
In 1932, he entered the University of Goettingen in Goettingen, Germany.
Then, from 1933 to 1935, he divided his time between the Universities of
Leipzig (1933-34) and Hamburg (1934-35), receiving his Ph.D degree in
Leipzig in 1936.
Professor Chow's long and distinguished work as a professional math
ematician began in China — with professorships at the National Central
University in Nanking (1936-37) and the National Tung-Chi University in
Shanghai (1946-47) — but ultimately led him to the United States, where
he joined the Mathematics faculty of the Johns Hopkins University in Balti
more, Maryland, first as an Associate Professor from 1948 to 1950, then as
a full Professor from 1950 until his retirement in 1977.
The late 1940s and early 1950s were a particularly active period for Chow
and his pioneering scholarship. He was a Visiting Member of the Institute
for Advanced Study in Princeton, NJ (1947-48, then again in 1954-55);
an invited speaker at the Conference in Algebraic Geometry and Algebraic
Number Theory at the University of Chicago (1949); an official delegate of
the Johns Hopkins University to the International Congress of Mathemati
cians hosted by Harvard University in Cambridge, Massachusetts, and an
invited speaker at the Harvard Conference on Algebraic Geometry which
immediately followed the Congress (1950); an invited member of the AMS
Summer Institute on Lie Groups and Lie Algebra held at Colby College in
Waterville, Maine (1953); an invited speaker at Princeton's Conference on
Algebraic Geometry in honor of Professor Solomon Lefschetz (1954); and
an invited member of the AMS Summer Institute on Algebraic Geometry
and Complex Varieties at the University of Colorado in Boulder (1954).
The middle and later portions of Chow's career were similarly produc
tive. In addition to serving as Chairman of the Math Department at Hopkins
from 1955 to 1965, he simultaneously enjoyed a long and fruitful relationship
with the American Journal of Mathematics — a publication whose direction
he would help to shape, as Editor-in-Chief, from 1953 to 1977. Lectures
at mathematics colloquia of leading universities in the northeastern United
States were also a common occurrence during this period, as were a vari
ety of other scientific activities, including the 1964 AMS Summer Institute
on Algebraic Geometry and Complex Varieties of the National Academy
X
of Sciences, in Woods Hole, MA, on Cape Cod, which Chow helped to
organize.
Professor Chow retired from Hopkins and was named Professor Emeritus
in 1977. He did, however, remain active in mathematical circles, serving
as a Visiting Professor at Hopkins during the Winter of 1977, as a Visiting
Professor at Purdue University in 1978, and as a part-time Visiting Professor
at Hopkins from 1979 to 1987. He died in August of 1995 at the age of 83.