The first edition of this book came out just as the apparatus of algebraic geometry was reaching a stage that permitted a lucid and concise account of the foundations of the subject. The author was no longer forced into the painful choice between sacrificing rigour of exposition or overloading the clear geometrical picture with cumbersome algebraic apparatus. 　　此书为英文版！

代数几何，ISBN：9787030029706，作者：（美）R.哈茨霍恩（Robin Hartshorne）著；冯克勤等译

《代数几何原理》主要内容：A third general principle was that this volume should be stir-contained.In particular any "hard" result that would be utilized should be fullyproved. A difficulty a student often faces in a subject as diverse as algebraic geometry is the profusion of cross-references, and this is one reason for attempting to be self-contained. Similarly, we have attempted to avoid allusions to, or statements without proofs of, related results. This book is in no way meant to be a survey of algebraic geometry, but rather is designed to develop a working facility with specific geometric questions.Our approach to the subject is initially analytic: Chapters 0 and 1 treat the basic techniques and results of complex manifold theory, with some emphasis on results applicable to projective varieties. Beginning in Chapter 2 with the theory of Riemann surfaces and algebraic curves, and continu-ing in Chapters 4 and 6 on algebraic surfaces and the quadric line complex, our treatment becomes increasingly geometric along classicallines. Chapters 3 and 5 continue the analytic approach, progressing to more special topics in complex manifolds.

H. CARTAN and J.-P. SERRE have shown how fundamental theoremson holomorphically complete manifolds (STEIN manifolds) can be for-mulated in terms of sheaf theory. These theorems imply many facts offunction theory because the domains of holomorphy are holomorphicallycomplete. They can also be applied to algebraic geometry because thecomplement of a hyperplane section of an algebraic manifold is holo-morphically complete. J.-P. SERRE has obtained important results onalgebraic manifolds by these and other methods. Recently many of hisresults have been proved for algebraic varieties defined over a field ofarbitrary characteristic. K. KODAIRA and D. C. SPENCER have alsoapplied sheaf theory to algebraic geometry with great success. Theirmethods differ from those of SERRE in that they use techniques fromdifferential geometry (harmonic integrals etc.) but do not make any useof the theory of STEIN manifolds. M. F. ATIVAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind onalgebraic manifolds with the help of sheaf theory.

This book provides an introduction to abstract algebraic geometry using the methods of schemes and cohomology. The main objects of study are algebraic varieties in an affine or projective space over an algebraically closed field; these are introduced in Chapter I, to establish a number of basic concepts and examples. Then the methods of schemes and cohomology are developed in Chapters II and III, with emphasis on applications rather than excessive generality. The last two chapters of the book (IV and V) use these methods to study topics in the classical theory of algebraic curves and surfaces. 　　本书为英文版。