Tying Bells on Characteristic Zero 1957–1961

Upon his return to Harvard in September of 1957, Zariski initiated what would later fondly be called his “famous seminar.” Using work that he had done in Japan, he led a small group of students on a forced march through what remained of unexplored territory in the older “real” world of characteristic zero, extending each result into the treacherous new world of characteristic p. (“He was tying bells on characteristic zero” is the way David Mumford remembered it.) Never shirking the slog through the swamp of characteristic p, he guided his students through questions of the existence of minimal nonsingular models in each birational equivalence class of surfaces.

They moved swiftly. Each student was required to prepare a seminar paper each week on a topic that had been announced only the previous week, although Zariski chose the actual speaker only at the last minute. Some fell by the wayside; others, like Michael Artin, Heisuke Hironaka, and David Mumford, were permanently converted to algebraic geometry.