TY - JOUR
T1 - A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles
AU - Chen, Zhangchi
N1 - Publisher Copyright:
© 2017, Mathematica Josephina, Inc.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Consider a domain Ω in Cn with n⩾ 2 and a compact subset K⊂ Ω such that Ω\ K is connected. We address the problem whether a holomorphic line bundle defined on Ω\ K extends to Ω. In 2013, Fornæss, Sibony, and Wold gave a positive answer in dimension n⩾ 3 , when Ω is pseudoconvex and K is a sublevel set of a strongly plurisubharmonic exhaustion function. However, for K of general shape, we construct counterexamples in any dimension n⩾ 2. The key is a certain gluing lemma by means of which we extend any two holomorphic line bundles which are isomorphic on the intersection of their base spaces.
AB - Consider a domain Ω in Cn with n⩾ 2 and a compact subset K⊂ Ω such that Ω\ K is connected. We address the problem whether a holomorphic line bundle defined on Ω\ K extends to Ω. In 2013, Fornæss, Sibony, and Wold gave a positive answer in dimension n⩾ 3 , when Ω is pseudoconvex and K is a sublevel set of a strongly plurisubharmonic exhaustion function. However, for K of general shape, we construct counterexamples in any dimension n⩾ 2. The key is a certain gluing lemma by means of which we extend any two holomorphic line bundles which are isomorphic on the intersection of their base spaces.
KW - Gluing lemma
KW - Hartogs’ extension
KW - Holomorphic line bundles
UR - https://www.scopus.com/pages/publications/85031420391
U2 - 10.1007/s12220-017-9923-z
DO - 10.1007/s12220-017-9923-z
M3 - 文章
AN - SCOPUS:85031420391
SN - 1050-6926
VL - 28
SP - 2624
EP - 2643
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -