In this paper we study Higgs and co-Higgs G-bundles on compact K\"ahler manifolds X. Our main results are: (1) If X is Calabi-Yau, and (E,θ) is a semistable Higgs or co-Higgs G-bundle on X, then the principal G-bundle E is semistable. In particular, there is a deformation retract of MH(G) onto M(G), where M(G) is the moduli space of semistable principal G-bundles with vanishing rational Chern classes on X, and analogously, MH(G) is the moduli space of semistable principal Higgs G-bundles with vanishing rational Chern classes. (2) Calabi-Yau manifolds are characterized as those compact K\"ahler manifolds whose tangent bundle is semistable for every K\"ahler class, and have the following property: if (E,θ) is a semistable Higgs or co-Higgs vector bundle, then E is semistable.
|Titolo:||Yang-Mills-Higgs connections on Calabi-Yau manifolds, II|
|Autori:||Biswas, I.; Bruzzo, U.; Graña Otero, B.; Lo Giudice, A.|
|Data di pubblicazione:||2016|
|Appare nelle tipologie:||1.1 Journal article|