Introduction to Geometric Invariant Theory

These notes originate in a series of lectures given at the Tokyo Metropolitan University and Seoul National University i

342 96 3MB

English Pages 147 Year 1994

Table of contents :
Dolgachev I.V. Introduction to geometric invariant theory (Seoul National University, 1994) ......Page 2
Notes of the Series of Lectures held at the Seoul National University ......Page 3
CONTENTS ......Page 5
Preface v ......Page 6
Introduction ix ......Page 7
Lecture 1. Algebraic groups 1 ......Page 10
Lecture 2. Algebraic group actions 9 ......Page 18
Lecture 3. Linearizations of actions 17 ......Page 26
Lecture 4. Quotients 30 ......Page 39
Lecture 5. Hilbert’s fourteenth problem 41 ......Page 50
Lecture 6. Stability 51 ......Page 60
Lecture 7. Numerical criterion of stability 60 ......Page 69
Lecture 8. Example: projective hypersurfaces 69 ......Page 78
Lecture 9. Example: configurations of linear subspaces 80 ......Page 89
Lecture 10. Toric varieties 97 ......Page 106
Lecture 11. Moduli space of curves 108 ......Page 117
References 136 ......Page 145
cover ......Page 1

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