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Classical Algebraic Geometry: a modern view

“The second growing category of work in America involves personal services. Computers and robots can’t do these jobs because they require care or attentiveness. Workers in other nations can’t do them because they must be done in person. Some personal-service workers need education beyond high school – nurses, physical ther- apists and medical technicians, for example. But most don’t, such as restaurant workers, cabbies, retail workers, security guards and hospital attendants. In contrast to that of symbolic analysts, the pay of most personal-service workers in the U.S. is stagnant or de- clining. That’s because the supply of personal-service workers is growing quickly, as more and more people who’d otherwise have factory. | Classical Algebraic Geometry a modern view IGORV. DOLGACHEV Preface The main purpose of the present treatise is to give an account of some of the topics in algebraic geometry which while having occupied the minds of many mathematicians in previous generations have fallen out of fashion in modern times. Often in the history of mathematics new ideas and techniques make the work of previous generations of researchers obsolete especially this applies to the foundations of the subject and the fundamental general theoretical facts used heavily in research. Even the greatest achievements of the past generations which can be found for example in the work of F. Severi on algebraic cycles or in the work of O. Zariski s in the theory of algebraic surfaces have been greatly generalized and clarified so that they now remain only of historical interest. In contrast the fact that a nonsingular cubic surface has 27 lines or that a plane quartic has 28 bitangents is something that cannot be improved upon and continues to fascinate modern geometers. One of the goals of this present work is then to save from oblivion the work of many mathematicians who discovered these classic tenets and many other beautiful results. In writing this book the greatest challenge the author has faced was distilling the material down to what should be covered. The number of concrete facts examples of special varieties and beautiful geometric constructions that have accumulated during the classical period of development of algebraic geometry is enormous and what the reader is going to find in the book is really only the tip of the iceberg a work that is like a taste sampler of classical algebraic geometry. It avoids most of the material found in other modern books on the subject such as for example 10 where one can find many of the classical results on algebraic curves. Instead it tries to assemble or in other words to create a compendium of material that either cannot be found is too dispersed to be .