Ebook: Collected Papers, Vol. 3: Topology of Curves and Surfaces, and Special Topics in the Theory of Algebraic Varieties

Oscar Zariski's earliest papers originally appeared in 1924 and have been followed by a steady accretion ever since. That at least four volumes are required to publish his collected papers is an index to his productiveness and persistence; that they have been collected at all is a tribute to their continuing importance in the field of algebraic geometry.

The first two volumes of Zariski's papers were published in 1973. Volume I, Foundations of Algebraic Geometry and Resolution of Singularities, was edited by H. Hironaka and D. Mumford, and Volume II, Holomorphic Functions and Linear Systems, was edited by M. Artin and D. Mumford.

The papers contained in this third volume were originally published between 1925 and 1966, but the heart of the book is a sequence of papers, topological in nature, that appeared during the period 1928-1937. Zariski writes that "the reader will find in the introduction by M. Artin and B. Mazur an illuminating discussion of these papers and of their impact on later work by other mathematicians. Their discussion includes, in particular, my papers dealing with the following three topics: (1) solvability in radicals of equations of certain plane curves; (2) the fundamental group of the residual space of plane algebraic curves; (3) the topology of the singularities of plane algebraic curves."

M. Artin (of MIT) and B. Mazur (of Harvard) both studied under Zariski at Harvard and have since become his colleagues. Their Introduction to this volume provides a useful perspective on Zariski's topological work and on this area of topology in general.

These volumes are included in the series Mathematicians of Our Time, under the general editorship of Gian-Carlo Rota. Other volumes in the series now published include papers by Paul Erdös, Einar Hille, Charles Loewner, Percy Alexander MacMahon, George Pólya, Hans Rademacher, Stanislaw Ulam, and Norbert Wiener.