Complex Geometry from Riemann to Kähler–Einstein and Calabi–Yau

Complex geometry has been extensively studied and developed since the 19th century. This volume examines the subject from a global, historical perspective.

It begins with an essay on the historical development of complex geometry, with extensive quotations of experts past and present, followed by a discussion of Calabi–Yau manifolds, and a look at Shing-Tung Yau as a writer and mathematician. Next, it presents a series of selected papers, beginning with Bernhard Riemann’s thesis on the foundation of complex analysis, and his masterpiece on the foundations of geometry, followed by numerous seminal papers of modern practitioners: Atiyah, Bott, Chern, Calabi, Chow, Donaldson, Hirzebruch, Kähler, Kodaira, Siu, Uhlenbeck, and Yau.

The volume concludes with a set of commentaries written by Yau, from his personal perspective, on the broad subject of complex geometry and its applications; and finally with an extensive list of papers on complex geometry from the 20th and 21st centuries, categorized by topic.