On projectivized vector bundles and positive holomorphic sectional curvature

We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature.

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Proceedings of the American Mathematical Society 2018-07, Vol.146 (7), p.2877-2882
Hauptverfasser:	ALVAREZ, ANGELYNN, HEIER, GORDON, ZHENG, FANGYANG
Format:	Artikel
Sprache:	eng
Schlagworte:	B. ANALYSIS
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

container_end_page	2882
container_issue	7
container_start_page	2877
container_title	Proceedings of the American Mathematical Society
container_volume	146
creator	ALVAREZ, ANGELYNN HEIER, GORDON ZHENG, FANGYANG
description	We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature.
doi_str_mv	10.1090/proc/13868
format	Article
fullrecord	<record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1090_proc_13868</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>90021372</jstor_id><sourcerecordid>90021372</sourcerecordid><originalsourceid>FETCH-LOGICAL-a385t-6821ff6ebf361db48f4bfd264f50496d4259590b67ba7bd4020d31aea26f5d003</originalsourceid><addsrcrecordid>eNp9kM1LAzEQxYMoWKsX70IuXoS1k4_NJkcpVoVCL3pekk1Ct2w3S9It6F9v1opHTzPDe2-Y-SF0S-CRgILFEEOzIEwKeYZmBKQshKTiHM0AgBZKMXWJrlLa5ZEoXs3QetPjHNq55tAe2y9n8TG3IWIz9rZzCeve4iGkNssOb0MX9iEO27bBaYqEXne4GeNRH8bortGF111yN791jj5Wz-_L12K9eXlbPq0LzWR5mE4i3gtnPBPEGi49N95SwX0JXAnLaalKBUZURlfGcqBgGdFOU-FLC8Dm6OG0t4khpeh8PcR2r-NnTaCeONQTh_qHQzbfncy7lP_6c6oMhLCKZv3-pOt9-m_PNyEHaGI</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On projectivized vector bundles and positive holomorphic sectional curvature</title><source>American Mathematical Society Publications (Freely Accessible)</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>JSTOR Mathematics & Statistics</source><source>Jstor Complete Legacy</source><source>American Mathematical Society Publications</source><creator>ALVAREZ, ANGELYNN ; HEIER, GORDON ; ZHENG, FANGYANG</creator><creatorcontrib>ALVAREZ, ANGELYNN ; HEIER, GORDON ; ZHENG, FANGYANG</creatorcontrib><description>We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/proc/13868</identifier><language>eng</language><publisher>American Mathematical Society</publisher><subject>B. ANALYSIS</subject><ispartof>Proceedings of the American Mathematical Society, 2018-07, Vol.146 (7), p.2877-2882</ispartof><rights>Copyright 2018, American Mathematical Society</rights><rights>2018 by the American Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a385t-6821ff6ebf361db48f4bfd264f50496d4259590b67ba7bd4020d31aea26f5d003</citedby><cites>FETCH-LOGICAL-a385t-6821ff6ebf361db48f4bfd264f50496d4259590b67ba7bd4020d31aea26f5d003</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttp://www.ams.org/proc/2018-146-07/S0002-9939-2018-13868-X/S0002-9939-2018-13868-X.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttp://www.ams.org/proc/2018-146-07/S0002-9939-2018-13868-X/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>68,69,314,778,782,801,830,23307,23311,27907,27908,58000,58004,58233,58237,77587,77589,77597,77599</link.rule.ids></links><search><creatorcontrib>ALVAREZ, ANGELYNN</creatorcontrib><creatorcontrib>HEIER, GORDON</creatorcontrib><creatorcontrib>ZHENG, FANGYANG</creatorcontrib><title>On projectivized vector bundles and positive holomorphic sectional curvature</title><title>Proceedings of the American Mathematical Society</title><description>We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature.</description><subject>B. ANALYSIS</subject><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kM1LAzEQxYMoWKsX70IuXoS1k4_NJkcpVoVCL3pekk1Ct2w3S9It6F9v1opHTzPDe2-Y-SF0S-CRgILFEEOzIEwKeYZmBKQshKTiHM0AgBZKMXWJrlLa5ZEoXs3QetPjHNq55tAe2y9n8TG3IWIz9rZzCeve4iGkNssOb0MX9iEO27bBaYqEXne4GeNRH8bortGF111yN791jj5Wz-_L12K9eXlbPq0LzWR5mE4i3gtnPBPEGi49N95SwX0JXAnLaalKBUZURlfGcqBgGdFOU-FLC8Dm6OG0t4khpeh8PcR2r-NnTaCeONQTh_qHQzbfncy7lP_6c6oMhLCKZv3-pOt9-m_PNyEHaGI</recordid><startdate>20180701</startdate><enddate>20180701</enddate><creator>ALVAREZ, ANGELYNN</creator><creator>HEIER, GORDON</creator><creator>ZHENG, FANGYANG</creator><general>American Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180701</creationdate><title>On projectivized vector bundles and positive holomorphic sectional curvature</title><author>ALVAREZ, ANGELYNN ; HEIER, GORDON ; ZHENG, FANGYANG</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a385t-6821ff6ebf361db48f4bfd264f50496d4259590b67ba7bd4020d31aea26f5d003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>B. ANALYSIS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>ALVAREZ, ANGELYNN</creatorcontrib><creatorcontrib>HEIER, GORDON</creatorcontrib><creatorcontrib>ZHENG, FANGYANG</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>ALVAREZ, ANGELYNN</au><au>HEIER, GORDON</au><au>ZHENG, FANGYANG</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On projectivized vector bundles and positive holomorphic sectional curvature</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2018-07-01</date><risdate>2018</risdate><volume>146</volume><issue>7</issue><spage>2877</spage><epage>2882</epage><pages>2877-2882</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M with positive holomorphic sectional curvature and any holomorphic vector bundle E over M, the projectivized vector bundle {\mathbb{P}}(E) admits a Kähler metric with positive holomorphic sectional curvature.</abstract><pub>American Mathematical Society</pub><doi>10.1090/proc/13868</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record>
fulltext	fulltext
identifier	ISSN: 0002-9939
ispartof	Proceedings of the American Mathematical Society, 2018-07, Vol.146 (7), p.2877-2882
issn	0002-9939 1088-6826
language	eng
recordid	cdi_crossref_primary_10_1090_proc_13868
source	American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; Jstor Complete Legacy; American Mathematical Society Publications
subjects	B. ANALYSIS
title	On projectivized vector bundles and positive holomorphic sectional curvature
url	https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T13%3A55%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20projectivized%20vector%20bundles%20and%20positive%20holomorphic%20sectional%20curvature&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.au=ALVAREZ,%20ANGELYNN&rft.date=2018-07-01&rft.volume=146&rft.issue=7&rft.spage=2877&rft.epage=2882&rft.pages=2877-2882&rft.issn=0002-9939&rft.eissn=1088-6826&rft_id=info:doi/10.1090/proc/13868&rft_dat=%3Cjstor_cross%3E90021372%3C/jstor_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=90021372&rfr_iscdi=true