2005/12/31 by R. P. Thomas · 1 citation
Mathematics · #math.AG #math.DG #math.SG #msc:14L24 #msc:53D20 #msc:53C07 #msc:32Q20
published as Surveys in Differential Geometry, 10 (2006): A Tribute to Professor S.-S. Chern. · Expanded version of talk at JDG 2005 conference, for "Surveys in Differential Geometry". 51 pages, 15 figures. Final version
arxiv created 2006/09/18 · arxiv updated 2009/12/01
These notes give an introduction to Geometric Invariant Theory and symplectic reduction, with lots of pictures and simple examples. We describe their applications to moduli of bundles and varieties, and their infinite dimensional analogues in gauge theory and the theory of special metrics on algebraic varieties. Donaldson's "quantisation" link between the infinite and finite dimensional situations is described, as are surprisingly strong connections between the bundle and variety cases.