Chapman and Hall/CRC
This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.
1. Introduction 2. The First Epoch—Prehistory (ca. 400 B.C.-1630 A.D.) 3. The Second Epoch—Exploration (1630-1795) 4. The Third Epoch—The golden age of projective geometry (1795-1850) 5. The Fourth Epoch—Riemann and birational geometry (1850-1866) 6. The Fifth Epoch—Development and chaos (1866-1920) 7. The Sixth Epoch—New structures in algebraic geometry (1920-1950) 8. The Seventh Epoch—Sheaves and schemes (1950- ) 9. Recent Results and Open Problems