The higher direct image sheaves of families of Hermite-Einstein vector bundles on compact Kähler manifolds are investigated. On the complement of a proper analytic subset of the base these sheaves induce holomorphic vector bundles which carry a natural hermitian metric. These metrics are generalizations of the Weil-Petersson metric on the base and fiberwise they are induced by the L2 inner products of harmonic forms. The curvatures of these metrics are computed and connections to moduli spaces of stable bundles are discussed. The main tool is the Hodge theory in holomorphic vector bundles over compact Kähler manifolds.
Sheaves and cohomology of sections of holomorphic vector bundles, general resultsHermite-Einstein-VektorbündelCurvature of direct image sheavesModuli spacesKrümmung von direkten BildgarbenKähler manifoldsHermite-Einstein bundlesStable bundlesWeil-Petersson-MetrikAnalytic moduli problemsAlgebraic moduli problems, moduli of vector bundlesWeil-Petersson metricStabile VektorbündelModulräume
Geiger, Thomas Wolfgang (1044940832): Krümmung von höheren direkten Bildgarben auf dem Modulraum der stabilen Vektorbündel. : Philipps-Universität Marburg 2013-12-04. DOI: https://doi.org/10.17192/z2013.0500.
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