Higgs bundles and holomorphic forms

✍ Scribed by Walter Seaman

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 180 KB
• Volume: 12
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(00)00018-8

✦ Synopsis

For a complex manifold X which has a holomorphic form of odd degree k, we endow E a = p a ( p,0) (X ) with a Higgs bundle structure θ given by θ(Z )(φ) := {i(Z ) } ∧ φ. The properties such as curvature and stability of these and other Higgs bundles are examined. We prove (Theorem 2, Section 2, for k > 1) E a and additional classes of Higgs subbundles of E a do not admit Higgs-Hermitian-Yang-Mills metric in any one of the cases: (i) deg(X ) < 0, (ii) deg(X ) = 0 and a nk + 1, or (iii) a nk + 1 and k 1 2 n + 1. We give examples of (noncompact) Kähler manifolds with the above Higgs structure which admit Higgs-Hermitian-Yang-Mills metrics. We also examine vanishing theorems for ( p, q)-forms with values in Higgs bundles.