The theory of sheaves, developed and applied to various topological problems by Leray 1), has recently been applied to algebraic geometry and to the theory of functions of several complex variables. These applications, due chiefly to Cartan, Serre, Kodaira, Spencer, Atiyah and Hodge have made possible a common systematic approach to both subjects. This book makes a further contribution to this development for algebraic geometry. In addition it contains applications of the results of Thom on cobordism of differentiable manifolds which are of independent interest. Sheaf theory and cobordism theory together provide the foundations for the present results on algebraic manifolds. This introduction gives an outline (0.1–0.8) of the results in the book. It does not contain precise definitions; these can be found by reference to the index. Remarks on terminology and notations used throughout the book are at the end of the introduction (0.9).
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