Birational geometry for number theorists
摘要
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.
引用
@article{arxiv.math/0701105,
title = {Birational geometry for number theorists},
author = {Dan Abramovich},
journal= {arXiv preprint arXiv:math/0701105},
year = {2007}
}
备注
CMI summer school in arithmetic geometry, Gottingen, 2006. Numerous corrections following referee's report