Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022
Ryushi Goto ^{[a]}
Moduli spaces of EinsteinHermitian generalized connections
over generalized Kähler manifolds of symplectic type
Pages: 611649
Received: 12 January 2022
Accepted in revised form: 30 May 2022
Mathematics Subject Classification: 53D18, 53D20, 53D17, 53C26.
Keywords: Generalized complex structure, generalized Kähler structure, moment map,
generalized EinsteinHermitian metric, Poisson structure, coHiggs bundles.
Author address:
[a]: Osaka University, Department of Mathematics, Graduate School of Science Toyonaka, Osaka, Japan.
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Abstract:
From a view point of the moment map, we shall introduce
the notion of EinsteinHermitian generalized connections over a generalized
Kähler manifold of symplectic type. We show that moduli spaces
of EinsteinHermitian generalized connections arise as the Kähler quotients.
The deformation complex of EinsteinHermitian generalized connections
is an elliptic complex and it turns out that the smooth part of
the moduli space is a finite dimensional Kähler manifold. The canonical
line bundle over a generalized Kähler manifold of symplectic type has the
canonical generalized connection and its curvature coincides with "the
scalar curvature as the moment map" which is defined in the previous paper
[10]. KählerRicci solitons provide examples of EinsteinHermitian
generalized connections and Einstein Hermitian coHiggs bundles are
also discussed.
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