Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove...Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E’=E|<sub> \D</sub> compatible with the parabolic structure, whose curvature is square integrable.展开更多
The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectivel...The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.展开更多
文摘Let M be a compact complex manifold of complex dimension two with a smooth K hler metric and D a smooth divisor on . If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E’=E|<sub> \D</sub> compatible with the parabolic structure, whose curvature is square integrable.
文摘The authors discuss the existence and classification of stable vector bundles of rank 3, with 2 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω3^2,d and w3 respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω3^2,4 and a complete discussion on the structure of ω3^3,2/3g＋2.
