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Twistor structures, \(tt^*\)-geometry and singularity theory. (English) Zbl 1151.14304

Donagi, Ron Y. (ed.) et al., From Hodge theory to integrability and TQFT tt*-geometry. International workshop From TQFT to tt* and integrability, Augsburg, Germany, May 25–29, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4430-4/hbk). Proceedings of Symposia in Pure Mathematics 78, 49-73 (2008).
Summary: We give an overview on the \(tt^*\)-geometry defined for isolated hypersurface singularities and tame functions via Brieskorn lattices. We discuss nilpotent orbits in this context, as well as classifying spaces of Brieskorn lattices and (limits of) period maps.
For the entire collection see [Zbl 1148.14002].

MSC:

14D07 Variation of Hodge structures (algebro-geometric aspects)
32S30 Deformations of complex singularities; vanishing cycles
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
32G20 Period matrices, variation of Hodge structure; degenerations
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