D. Mumford’s Geometric Invariant Theory

  • Eckart Viehweg
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 30)


We recall some basic definitions and results from geometric invariant theory, all contained in the first two chapters of D. Mumford’s book [59]. For the statements which are used in this monograph, except for those coming from the theory of algebraic groups, such as the finiteness of the algebra of invariants under the action of a reductive group, we include proofs. Usually we just reproduce the arguments given by Mumford in [59] (hopefully without adding some inaccuracies). Other sources of inspiration are [26], [64], [66] and [71].


Algebraic Group Local Quotient Zariski Topology Invertible Sheaf Open Subscheme 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Eckart Viehweg
    • 1
  1. 1.Fachbereich 6, MathematikUniversität-Gesamthochschule EssenEssenGermany

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