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This edition has been completely revised and much of it rewritten, and, while the essential principles remain unchanged, some slight departures from previously expressed opinions may be noted; for in the years that have elapsed since the first edition saw the light, some notable advances have been made in rational therapeutics and dietetics, and no one can afford to lag behind the car of Progress.
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This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: “There is no royal road to geometry!” The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royal road to algebraic geometry. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck’s theory of schemes. Contemporary homological tools are explained. The reader will follow a directed path leading up to the main elements of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest scientific experience of a lifetime!
When Richard Halliburton graduated from college, he chose adventure over a career, traveling the world with almost no money. The Royal Road to Romance chronicles what happened as a result, from a breakthrough Matterhorn ascent to being jailed for taking forbidden pictures on Gibraltar. Halliburton's literary career developed out of his meticulous logging of events that occurred on his own adventures. This book, his first, an account of his travels in 1921-23, was a best-seller for three years and was translated into 15 languages.