Fundamentals of Algebraic Surfaces

Fundamental properties of algebraic surfaces are collected and reviewed, such as curves on a surface, divisors and linear systems and the Riemann–Roch theorem. An elementary proof of Noether’s formula is also given.

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Kunihiko Kodaira

Theory of Algebraic Surfaces

SpringerBriefs in Mathematics Series Editors Nicola Bellomo, Torino, Italy Michele Benzi, Pisa, Italy Palle Jorgensen, Iowa, USA Tatsien Li, Shanghai, China Roderick Melnik, Waterloo, Canada Otmar Scherzer, Linz, Austria Benjamin Steinberg, New York, USA Lothar Reichel, Kent, USA Yuri Tschinkel, New York, USA George Yin, Detroit, USA Ping Zhang, Kalamazoo, USA

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Kunihiko Kodaira

Theory of Algebraic Surfaces

Kunihiko Kodaira University of Tokyo Tokyo, Japan Translated by Kazuhiro Konno Takatsuki, Japan

ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-981-15-7379-8 ISBN 978-981-15-7380-4 (eBook) https://doi.org/10.1007/978-981-15-7380-4 © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Notes taken by Shigeho Yamashima

Kunihiko Kodaira at his home in Tokyo, 1990 © Springer Japan

Foreword

In the academic year 1967, Kunihiko Kodaira gave a course of lectur