Incorporated in this 2003 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. Amongst other
things this volume includes an improved presentation of the
classical foundations of invarant 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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