Birational geometry for number theorists
Abstract
Description
Awfully idiosyncratic lecture notes from CMI summer school in arithmetic geometry July 31-August 4, 2006.
Does not include: rationality problems, techniques of the minimal model problem and much of the rest.
Includes: Lecture 0: geometry and arithmetic of curves
Lecture 1: Kodaira dimension and properties, rational connectendess, Lang's and Campana's conjectures.
Lecture 2: Campana's program; Campana constellations framed in terms of b-divisors, to allow for a definition of Kodaira dimension directly on the base. A speculative notion of firmaments which may deserve further investigation, especially the arithmetic side.
Lecture 3: the minimal model program: very short discussion of bend-and-break; even shorter discussion of finite generation and the existence of flip.
Lecture 4: Vojta's conjectures, Campana's conjectures, and ABC.
CMI summer school in arithmetic geometry, Gottingen, 2006. Numerous corrections following referee's report
CMI summer school in arithmetic geometry, Gottingen, 2006. Numerous corrections following referee's report