Yang-Mills connections on compact complex tori

2014/11/11 by Indranil Biswas, Biswas, Indranil
Mathematics · #14L10 #32L05 #53C07 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:14L10 #msc:32L05 #msc:53C07

paper · pdf · doi:10.48550/arxiv.1411.2882

Journal of Topology and Analysis (to appear)

arxiv created 2014/11/11 · arxiv updated 2014/11/12

Abstract

Let G be a connected reductive complex affine algebraic group and K⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (E_G ,θ) a polystable Higgs G-bundle on M. Take any C^∞ reduction of structure group E_K ⊂ E_G to the subgroup K that solves the Yang--Mills equation for (E_G ,θ). We prove that the principal G-bundle E_G is polystable and the above reduction E_K solves the Einstein--Hermitian equation for E_G. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (E_G , θ) on a compact connected Calabi--Yau manifold, the underlying principal G-bundle E_G is semistable (respectively, polystable).

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