电力拖动自动控制系统习题例题集.pdf

London Mathematical Society Student Texts. 12
Undergraduate Algebraic
Geometry
Miles Reid, Mathematical Institute, University of Warwick
CAMBRIDGE UNIVERSITY PRESS
Cambridge
New York New Rochelle Melbourne Sydney
Published by the Press Syndicate of the University of Cambridge
The Pitt Building, Trumpington Street, Cambridge CB2 IRP
32 East 57th Street, New York, NY 10022, USA
10, Stamford Road, Oakleigh, Melbourne 3166, Australia
0 Cambridge University Press 1988
First published 1988
Printed in Great Britain at the University Press, Cambridge
Library of Congress cataloging in publication data: available
British Library cataloguing in publication data:
Reid, Miles
Undergraduate algebraic geometry
1. Algebraic geometry
I. Title II. Series
’5
ISBN 0 521 35559 1 Hardcover
ISBN 0 521 35662 8 Paperback
Preface
There are several good recent textbooks on algebraic geometry at
the graduate level, but not (to my knowledge) any designed for an
undergraduate course. Humble notes are from a course given in two
essive years in the 3rd year of the Warwick undergraduate math
course, and are intended as a self-contained introductory textbook.
vii
Contents
$0. Woffle . . . . . . . . . . . . . . . . . . . . . . . . . 1
Reasons for studying algebraic geometry, the ‘subset’  problem; different
categories of geometry, need mutative algebra, partially defined function;
character of the author. Prerequisites, relations with other courses, list of books.
Chapter I. Playing with plane curves . . . . . . . . . . . . 9
$1. Plane tonics . . . . . . . . . . . . . . . . . . . . . . . 9
General familiarity with (P2 and homogeneous coordinates, relation of A2 to
tP22; parametrisation, every smooth conic C c tP2 is 2 [P l. Easy cases of
Btzout’s theorem: line n curve of degree d = d points, conic n curve of degree d
= 2d points; linear system of tonics through P I,.. P n
$2. Cubits and the group law . . . . . . . . . . . . . .