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Metrics on moduli spaces. (English) Zbl 0618.32017

Algebraic geometry, Proc. Lefschetz Centen. Conf., Mexico City/Mex. 1984, Pt. I, Contemp. Math. 58, 157-178 (1986).
[For the entire collection see Zbl 0588.00015.]
The main result of this paper is the observation due to the author: ”A hyper-Kähler metric is shown to exist on an open set of the moduli space of all flat bundles on a Riemann surface. The moduli space of irreducible unitary connections together with its natural metric is the fixed point set of a circle action in this space”.
Reviewer: P.Cherenack

MSC:

32G13 Complex-analytic moduli problems
14D20 Algebraic moduli problems, moduli of vector bundles
53B35 Local differential geometry of Hermitian and Kählerian structures
32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)
32L25 Twistor theory, double fibrations (complex-analytic aspects)
53C80 Applications of global differential geometry to the sciences

Citations:

Zbl 0588.00015