An Introduction to Invariants and Moduli

This 2003 volume consists of the first two volumes of Mukai's series on moduli theory.

Shigeru Mukai (Author), W. M. Oxbury (Translated by)

9781107406360, Cambridge University Press

Paperback / softback, published 16 August 2012

524 pages
22.9 x 15.2 x 3 cm, 0.76 kg

Review of the hardback: 'The book contains a great amount of material, but it remains very readable. The author has obviously put a lot of effort into making even the complicated topics accessible.' Gábor Megyesi, UMIST

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.

1. Invariants and moduli
2. Rings and polynomials
3. Algebraic varieties
4. Algebraic groups and rings of invariants
5. Construction of quotient spaces
6. Global construction of quotient varieties
7. Grassmannians and vector bundles
8. Curves and their Jacobians
9. Stable vector bundles on curves
10. Moduli functors
11. Intersection numbers and the Verlinde formula
12. The numerical criterion and its applications.

Subject Areas: Topology [PBP], Geometry [PBM]