TY - JOUR
T1 - Weakly 1-completeness of holomorphic fiber bundles over compact Kähler manifolds
AU - Seo, Aeryeong
N1 - Publisher Copyright:
© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.
PY - 2022/10
Y1 - 2022/10
N2 - Diederich and Ohsawa (Publ. Res. Inst. Math. Sci. 21 (1985), no. 4, 819–833) proved that every disc bundle over a compact Kähler manifold is weakly 1-complete. In this paper, under certain conditions, we generalize this result to the case of fiber bundles over compact Kähler manifolds whose fibers are bounded symmetric domains. In particular, if the representation related to the fiber bundle is reductive, then it has a plurisubharmonic exhaustion function. If the bundle is obtained by the diagonal action on the product of bounded symmetric domains, we are able to show that it is hyperconvex.
AB - Diederich and Ohsawa (Publ. Res. Inst. Math. Sci. 21 (1985), no. 4, 819–833) proved that every disc bundle over a compact Kähler manifold is weakly 1-complete. In this paper, under certain conditions, we generalize this result to the case of fiber bundles over compact Kähler manifolds whose fibers are bounded symmetric domains. In particular, if the representation related to the fiber bundle is reductive, then it has a plurisubharmonic exhaustion function. If the bundle is obtained by the diagonal action on the product of bounded symmetric domains, we are able to show that it is hyperconvex.
UR - http://www.scopus.com/inward/record.url?scp=85132427280&partnerID=8YFLogxK
U2 - 10.1112/jlms.12635
DO - 10.1112/jlms.12635
M3 - Article
AN - SCOPUS:85132427280
SN - 0024-6107
VL - 106
SP - 2305
EP - 2341
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
IS - 3
ER -