Chapters on algebraic surfaces 论文

摘要

This is a first graduate course in algebraic geometry. It aims to give the student a lift up into the subject at the research level, with lots of interesting topics taken from the classification of surfaces, and a human-oriented discussion of some of the technical foundations, but with no pretence at an exhaustive treatment. I hope that graduate students can use some of these chapters as a reader through the subject, maybe in parallel with a conventional textbook. The early chapters introduce topics that are useful throughout projective and algebraic geometry, make little demands, and lead to fun calculations. The intermediate chapters introduce elements of the technical language gradually, whereas the later chapters get into the substance of the classification of surfaces. I have given several sets of lectures on algebraic geometry at the graduate or advanced undergraduate level over the last few years. The 1993 Park City summer school, with the challenge of taking a numerous audience through from a basic level up to the sky, was perhaps the most fun. I have thus accumulated a considerable body of notes, without ever having time to organise the material properly in book