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A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles
Consider a domain Ω in C n 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 sub...
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| Published in: | The Journal of geometric analysis 2018-07, Vol.28 (3), p.2624-2643 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c389t-68554af0068a40633ba5dff000dbd8fbddda101b4c3c3f617dd0fed723a659fb3 |
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| cites | cdi_FETCH-LOGICAL-c389t-68554af0068a40633ba5dff000dbd8fbddda101b4c3c3f617dd0fed723a659fb3 |
| container_end_page | 2643 |
| container_issue | 3 |
| container_start_page | 2624 |
| container_title | The Journal of geometric analysis |
| container_volume | 28 |
| creator | Chen, Zhangchi |
| description | Consider a domain
Ω
in
C
n
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. |
| doi_str_mv | 10.1007/s12220-017-9923-z |
| format | article |
| fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_02455026v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2077517516</sourcerecordid><originalsourceid>FETCH-LOGICAL-c389t-68554af0068a40633ba5dff000dbd8fbddda101b4c3c3f617dd0fed723a659fb3</originalsourceid><addsrcrecordid>eNp1kN9KwzAUxosoOKcP4F3AKy-qJ0mTrpdzTDsYeDPBu5A2ydbRNTXpZNuVr-Hr-SRmVPRKOHD-8Ps-Dl8UXWO4wwDpvceEEIgBp3GWERofTqIBZiyLAcjraZiBQcwzws-jC-_XAAmnSTqIZmM0sdum007v5KatNeosyqXr7NJ_fXyixb7VaLrrdOMr2yBrUG5ru7GuXVUlmleNRg_bRtXaX0ZnRtZeX_30YfTyOF1M8nj-_DSbjOdxSUdZF_MRY4k0AHwkE-CUFpIpE3ZQhRqZQiklMeAiKWlJDcepUmC0SgmVnGWmoMPotvddyVq0rtpItxdWViIfz8XxBiRhDAh_x4G96dnW2bet9p1Y261rwnuCQJoyHIoHCvdU6az3TptfWwzimK7o0xUhXXFMVxyChvQaH9hmqd2f8_-ib6A7fZ0</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2077517516</pqid></control><display><type>article</type><title>A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles</title><source>Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List</source><creator>Chen, Zhangchi</creator><creatorcontrib>Chen, Zhangchi</creatorcontrib><description>Consider a domain
Ω
in
C
n
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.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-017-9923-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Bundles ; Bundling ; Complex Variables ; Convex and Discrete Geometry ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Exhaustion ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Gluing ; Mathematical analysis ; Mathematics ; Mathematics and Statistics</subject><ispartof>The Journal of geometric analysis, 2018-07, Vol.28 (3), p.2624-2643</ispartof><rights>Mathematica Josephina, Inc. 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c389t-68554af0068a40633ba5dff000dbd8fbddda101b4c3c3f617dd0fed723a659fb3</citedby><cites>FETCH-LOGICAL-c389t-68554af0068a40633ba5dff000dbd8fbddda101b4c3c3f617dd0fed723a659fb3</cites><orcidid>0000-0003-4475-849X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,27901,27902</link.rule.ids><backlink>$$Uhttps://hal.science/hal-02455026$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Chen, Zhangchi</creatorcontrib><title>A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles</title><title>The Journal of geometric analysis</title><addtitle>J Geom Anal</addtitle><description>Consider a domain
Ω
in
C
n
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.</description><subject>Abstract Harmonic Analysis</subject><subject>Bundles</subject><subject>Bundling</subject><subject>Complex Variables</subject><subject>Convex and Discrete Geometry</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Exhaustion</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Gluing</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kN9KwzAUxosoOKcP4F3AKy-qJ0mTrpdzTDsYeDPBu5A2ydbRNTXpZNuVr-Hr-SRmVPRKOHD-8Ps-Dl8UXWO4wwDpvceEEIgBp3GWERofTqIBZiyLAcjraZiBQcwzws-jC-_XAAmnSTqIZmM0sdum007v5KatNeosyqXr7NJ_fXyixb7VaLrrdOMr2yBrUG5ru7GuXVUlmleNRg_bRtXaX0ZnRtZeX_30YfTyOF1M8nj-_DSbjOdxSUdZF_MRY4k0AHwkE-CUFpIpE3ZQhRqZQiklMeAiKWlJDcepUmC0SgmVnGWmoMPotvddyVq0rtpItxdWViIfz8XxBiRhDAh_x4G96dnW2bet9p1Y261rwnuCQJoyHIoHCvdU6az3TptfWwzimK7o0xUhXXFMVxyChvQaH9hmqd2f8_-ib6A7fZ0</recordid><startdate>20180701</startdate><enddate>20180701</enddate><creator>Chen, Zhangchi</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0003-4475-849X</orcidid></search><sort><creationdate>20180701</creationdate><title>A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles</title><author>Chen, Zhangchi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c389t-68554af0068a40633ba5dff000dbd8fbddda101b4c3c3f617dd0fed723a659fb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Bundles</topic><topic>Bundling</topic><topic>Complex Variables</topic><topic>Convex and Discrete Geometry</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Exhaustion</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Gluing</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Zhangchi</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>The Journal of geometric analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Zhangchi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles</atitle><jtitle>The Journal of geometric analysis</jtitle><stitle>J Geom Anal</stitle><date>2018-07-01</date><risdate>2018</risdate><volume>28</volume><issue>3</issue><spage>2624</spage><epage>2643</epage><pages>2624-2643</pages><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>Consider a domain
Ω
in
C
n
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.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-017-9923-z</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0003-4475-849X</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | The Journal of geometric analysis, 2018-07, Vol.28 (3), p.2624-2643 |
| issn | 1050-6926 1559-002X |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_02455026v1 |
| source | Springer Nature:Jisc Collections:Springer Nature Read and Publish 2023-2025: Springer Reading List |
| subjects | Abstract Harmonic Analysis Bundles Bundling Complex Variables Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Exhaustion Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Gluing Mathematical analysis Mathematics Mathematics and Statistics |
| title | A Counterexample to Hartogs’ Type Extension of Holomorphic Line Bundles |
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