Complex Algebraic Surfaces (London Mathematical Society Student Texts Book 34) 2nd Edition by Arnaud Beauville (PDF)

Description

Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor Beauville gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.

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⭐This was a nice offer. They price corresponds to the book. Excellent business, I’d buy again.

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⭐曲面の交差理論やRiemann-Rochから始まり、Enriquesによる複素代数曲面の分類理論を層係数コホモロジーなどを使って現代風に説明する本。この本を読むためには、Zariski主定理やStein分解といったHartshorneに書いてあるような、代数幾何における有名な基本定理を知っておく必要はありますし、曲線のRiemann-Rochは当然として曲線のJacobianとかAbelの定理といった最低限度のRiemann面の知識も要るでしょう。代数幾何の基本的な定理や交差理論、などについて最初から全て自分で証明できるほど理解しようとすると大変ですが、使いこなしていくうちに当たり前に思えてくる部分もあります。ゼロから論理を追って悩むよりは、様々な道具を使って曲面に慣れ親しむという態度で勉強していってみると非常にいい本だと思います。

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