From a May 1989 symposium at Sundance, Utah, 13 papers review the 20-year interaction between the fields of complex geometry and Lie theory, emphasizing their links with Hodge theory. Some of the topics are the quartic double solid, curvature for period domains, and the ubiquity of variations of Hodge structure. No index. Annotation copyright Book News, Inc. Portland, Or.
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Enrico Arbarello and Corrado De Concini, Abelian varieties, infinite-dimensional Lie algebras, and the heat equation; Robert L Bryant, Two exotic holonomies in dimension four, path geometries, and twistor theory; Herbert Clemens, The quartic double solid revisited; Robert Friedman, On threefolds with trivial canonical bundle; H Garland and G J Zuckerman, Representations of Heisenberg systems and vertex operators; Phillip A Griffiths, Some aspects of exterior differential systems; Richard M Hain, Algebraic cycles and extensions of variations of mixed Hodge structure; E Looijenga and M Rapoport, Weights in the local cohomology of Baily-Borel compactification; C A M Peters, Curvature for period domains; Masa-Hiko Saito and Steven Zucker, On the Tortelli problem for fiber spaces; Morihiko Saito, Hodge conjecture and mixed motives. I; Rob Schrauwen, Joseph Steenbrink, and Jan Stevens, Spectral pairs and the topology of curve singularities; Carlos T Simpson, The ubiquity of variations of Hodge structure.
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