Journal article
Higgs bundles and holomorphic forms
Differential geometry and its applications, Vol.12(3), pp.291-311
2000
DOI: 10.1016/S0926-2245(00)00018-8
Abstract
For a complex manifold X which has a holomorphic form
ϖ of odd degree k , we endow
E
a
=⊕
p≥
a
Λ
(
p,0)
(
X) with a Higgs bundle structure
θ given by
θ(
Z)(
φ):={
i(
Z)
ϖ}∧
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≤
n−
k+1 , or (iii)
a≤
n−
k+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.
Details
- Title: Subtitle
- Higgs bundles and holomorphic forms
- Creators
- Walter Seaman - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Differential geometry and its applications, Vol.12(3), pp.291-311
- DOI
- 10.1016/S0926-2245(00)00018-8
- ISSN
- 0926-2245
- eISSN
- 1872-6984
- Publisher
- Elsevier B.V
- Language
- English
- Date published
- 2000
- Academic Unit
- Mathematics
- Record Identifier
- 9984241150902771
Metrics
8 Record Views