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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"All together, this is a marvellous and masterly introduction to moduli theory and its allied invariant theory. The exposition fascinates by great originality, glaring expertise, art of easiness and lucidity, up-to-dateness, reader-friendliness, and power of inspiration." --Werner Kleinert, Zentralblatt MATH
Language Notes
Text: English (translation)
Original Language: Japanese
Original Language: Japanese
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This chapter explores some examples of parameter spaces which can be constructed by elementary means and with little previous knowledge as an introduction to the general theory developed from Chapter 3 onwards. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
elementary sheaf, linear reductivity, secant numbers, projective quotient, geometric reductivity, standard line bundle, affine quotient, nonsingular algebraic curve, semistable points, line subbundle, projective spectrum, affine open cover, binary quartics, moduli functor, divisor type, distribution algebra, unique factorisation domain, quotient variety, coarse moduli space, invariant rational functions, moduli theory, affine algebraic group, algebraic group acting, regular elsewhere, stable vector bundles Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Liouville's Theorem, Proof Suppose, Hilbert's Nullstellensatz, Valuative Criterion, Hilbert's Basis Theorem, Kodaira Vanishing Theorem, Proof First, Proof Pick, Spm Rred New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter explores some examples of parameter spaces which can be constructed by elementary means and with little previous knowledge as an introduction to the general theory developed from Chapter 3 onwards. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
elementary sheaf, linear reductivity, secant numbers, projective quotient, geometric reductivity, standard line bundle, affine quotient, nonsingular algebraic curve, semistable points, line subbundle, projective spectrum, affine open cover, binary quartics, moduli functor, divisor type, distribution algebra, unique factorisation domain, quotient variety, coarse moduli space, invariant rational functions, moduli theory, affine algebraic group, algebraic group acting, regular elsewhere, stable vector bundles Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Liouville's Theorem, Proof Suppose, Hilbert's Nullstellensatz, Valuative Criterion, Hilbert's Basis Theorem, Kodaira Vanishing Theorem, Proof First, Proof Pick, Spm Rred New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 29
books:
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2
books
cite this book:
- Geometric Invariant Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) by David Mumford in Front Matter, and Back Matter
- Algebraic Geometry (Lecture Notes in Pure and Applied Mathematics) by Peter E. Newstead in Back Matter (1), and Back Matter (2)
- Number theory, Volume 20 (Pure and Applied Mathematics) by Author Unknown in Back Matter
- Introduction to Toric Varieties. (AM-131) by William Fulton in Back Matter
- Principles of Algebraic Geometry by Phillip Griffiths in Back Matter
See all 29 books this book cites
- Geometric And Combinatorial Aspects Of Commutative Algebra (Lecture Notes in Pure and Applied Mathematics) by Jurgen Herzog on page 209
- Introduction to the Mori Program by Kenji Matsuki in Back Matter
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