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Harmonic bundles on noncompact curves. (English) Zbl 0713.58012
This paper carries out a program outlined in the author’s paper in J. Am. Math. Soc. 1, No.4, 867-918 (1988; Zbl 0669.58008): extending to noncompact algebraic curves X the known correspondence between Higgs bundles and local systems. The main problem is the behaviour of certain singularities at the punctures of X. It builds on the theorem of Narasimhan-Seshadri on stable vector bundles, the theory of harmonic maps of Riemann surfaces, variations of Hodge structures, and differential equations with regular singularities. All together, here is a marvellous example of interrelationships between algebraic/differential geometry and analysis.
Reviewer: J.Eells

MSC:
58E20 Harmonic maps, etc.
14E20 Coverings in algebraic geometry
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
14D07 Variation of Hodge structures (algebro-geometric aspects)
58A14 Hodge theory in global analysis
30F99 Riemann surfaces
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References:
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