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Krümmung von höheren direkten Bildgarben auf dem Modulraum der stabilen Vektorbündel
Die höheren direkten Bildgarben von Familien von Hermite-Einstein-Vektorbündeln auf kompakten Kählermannigfaltigkeiten werden untersucht. Außerhalb einer echten analytischen Teilmenge der Basis induzieren diese Garben holomorphe Vektorbündel, die eine natürliche hermitesche Metrik tragen. Diese Metr...
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| Format: | Doctoral Thesis |
| Language: | German |
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Philipps-Universität Marburg
2013
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| Online Access: | PDF Full Text |
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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.