Kahler structure on moduli spaces of principal bundles

Biswas, Indranil ; Schumacher, Georg (2007) Kahler structure on moduli spaces of principal bundles Differential Geometry and its Applications, 25 (2). pp. 136-146. ISSN 0926-2245

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S09262...

Related URL: http://dx.doi.org/10.1016/j.difgeo.2006.05.001


Let M be a moduli space of stable principal G-bundles over a compact Kahler manifold (X,ω X), where G is a reductive linear algebraic group defined over C. Using the existence and uniqueness of a Hermite-Einstein connection on any stable G-bundle P over X, we have a Hermitian form on the harmonic representatives of H1(X,ad(P)), where ad (P) is the adjoint vector bundle. Using this Hermitian form a Hermitian structure M on is constructed; we call this the Petersson-Weil form. The Petersson-Weil form is a Kahler form, a fact which is a consequence of a fiber integral formula that we prove here. The curvature of the Petersson-Weil Kahler form is computed. Some further properties of this Kahler form are investigated.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Principal Bundle; Moduli Space; Petersson-weil Form
ID Code:3483
Deposited On:12 Oct 2010 04:31
Last Modified:16 May 2016 14:16

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