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 V|fe World Scientific »• NNeeww J Jeersrseeyy •L Loonnddoonn'S • iSnien gapore • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. THE COLLECTED PAPERS OF WEI-LIANG CHOW Copyright © 2002 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. 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 It also includes: • Chow's bibliography of all his publications in mathematics, except for, his unpublished manuscript [Ch 55c] that is posted at http://mathnt.mat.j hu.edu/mathnew/Chow/; • Chow's biography in dates; • Chern's remarks on Chow, previously published in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.