The Collected Papers of Wei-Liang Chow

by Chow, Wei-Liang; Shokurov, Vyacheslav V.; Chern, Shiing-Shen; Chern, Shiing-Shen

• ISBN13: 9789812380944
• ISBN10: 9812380949
• Format: Hardcover
• Copyright: 2002-12-01
• Publisher: Imperial College Pr

Summary

This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow's name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow's theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow's theorem -- that a compact analytic variety in a projective space is algebraic -- is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.

Table of Contents

Preface	vii
Biography	ix
Zur algebraische Geometrie IX; English translation by Wen-ling Huang	1	(13)
van der Waerden
Die geometrische Theorie der algebraischen Funktionen fur beliebige vollkommene Korper	14	(28)
Einfacher topologischer Beweis des Fundamentalsatzes der Algebra	42	(1)
Uber die Multiplizitat der Schnittpunkte von Hyperflachen	43	(4)
Uber systeme von linearen partiellen Differentialgleichungen erster Ordnung	47	(8)
On Electric Networks	55	(19)
On the Algebraical Braid Group	74	(5)
On Compact Complex Analytic Varieties	79	(22)
On the Geometry of Algebraic Homogeneous Spaces	101	(36)
Uber die Losbarkeit gewisser algebraischer Gleichungssysteme	137	(4)
On the Genus of Curves of an Algebraic System	141	(4)
On the Defining Field of a Divisor in an Algebraic Variety	145	(3)
Algebraic Systems of Positive Cycles in an Algebraic Variety	148	(37)
On the Quotient Variety of an Abelian Variety	185	(6)
On Picard Varieties	191	(15)
On Analytic Surfaces with Two Independent Meromorphic Functions	206	(7)
Kodaira
On the Fundamental Group of an Algebraic Variety	213	(11)
The Jacobian Variety of An Algebraic Curve	224	(24)
Remarks on my paper ``The Jacobian Variety of an Algebraic Curve''	248	(3)
On Abelian Varieties over Function Fields	251	(5)
Abelian Varieties over Function Fields	256	(23)
On Equivalence Classes of Cycles in an Algebraic Variety	279	(30)
Algebraic Varieties with Rational Dissections	309	(4)
On the Projective Embedding of Homogeneous Varieties	313	(6)
On the Principle of Degeneration in Algebraic Geometry	319	(10)
On the Birational Equivalence of Curves under Specialization	329	(4)
S. Lang
The Criterion for Unit Multiplicity and a Generalization of Hensel's Lemma	333	(14)
On the Theorem of Bertini for Local Domains	347	(5)
Cohomology Theory of Varieties over Rings	352	(5)
Igusa
On the Connectedness Theorem in Algebraic Geometry	357	(42)
On the Real Traces of Analytic Varieties	399	(11)
On Unmixedness Theorem	410	(24)
On Meromorphic Maps of Algebraic Varieties	434	(13)
On the Algebraicity of Certain Ringed Spaces	447	(16)
Correction to ``On the Algebraicity of Certain Ringed Spaces''	463	(2)
Formal Functions on Homogeneous Spaces	465	(16)
Shiing Shen Chern as Friend and Mathematician, A Reminiscence on the Occasion of his 80th Birthday	481	(10)
Wei-Liang Chow, 1911--1995	491	(2)
Comments on Chow's Work	493	(8)
Wei-Liang Chow's bibliography	501	(4)
Permission	505