Connections on principal bundles over Kähler manifolds with antiholomorphic involution. (English) Zbl 1093.32007
This is almost exactly the author’s abstract, which is perfect: Let \(M\) be a connected compact Kähler manifold equipped with an antiholomorphic involution \(\tau\) and \(G\) a complex reductive group with a fixed real structure. Here the author considers holomorphic principal \(G\)-bundles equipped with a lift of \(\tau\) to an antiholomorphic involution of \(E_G\). He extends the notion of polystability to such bundles and shows that polystability is equivalent to the existence of an Einstein-Hermitian connection compatible with the involution. When \(\dim (X) = 1\) he proves a criterion for such a bundle to have a holomorphic connection compatible with the involution.
Reviewer: Edoardo Ballico (Povo)
MSC:
| 32L05 | Holomorphic bundles and generalizations |
| 32M05 | Complex Lie groups, group actions on complex spaces |
| 14J60 | Vector bundles on surfaces and higher-dimensional varieties, and their moduli |
| 14P99 | Real algebraic and real-analytic geometry |
| 32J27 | Compact Kähler manifolds: generalizations, classification |
Keywords:
principal bundle; aniholomorphic involution; polystability; Kähler manifold; real principal bundle; connection on a principal bundleReferences:
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