An Introduction to Invariants and Moduli

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Cambridge University Press, Sep 8, 2003 - Mathematics - 503 pages
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Incorporated in this volume are the first two books in Mukai's series on Moduli Theory. The notion of a moduli space is central to geometry. However, its influence is not confined there; for example, the theory of moduli spaces is a crucial ingredient in the proof of Fermat's last theorem. Researchers and graduate students working in areas ranging from Donaldson or Seiberg-Witten invariants to more concrete problems such as vector bundles on curves will find this to be a valuable resource. Among other things this volume includes an improved presentation of the classical foundations of invariant theory that, in addition to geometers, would be useful to those studying representation theory. This translation gives an accurate account of Mukai's influential Japanese texts.
 

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Contents

Invariants and moduli
1
Rings and polynomials
51
Algebraic varieties
77
Algebraic groups and rings of invariants
116
The construction of quotient varieties
158
The projective quotient
181
The numerical criterion and some applications
211
Grassmannians and vector bundles
234
Curves and their Jacobians
287
Stable vector bundles on curves
348
Moduli functors
398
Intersection numbers and the Verlinde formula
437
Bibliography
487
Index
495
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