A Cayley--Bacharach theorem and plane configurations

A Cayley--Bacharach theorem and plane configurations

In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley–Bacharach condition. In particular, by bounding the number of points satisfying the Cayley–Bacharach condition, we force them to lie on unions of low-dimensional linear spaces. These result...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the American Mathematical Society 2022-11, Vol.150 (11), p.4603-4618
Hauptverfasser: Levinson, Jake, Ullery, Brooke
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 4618
container_issue 11
container_start_page 4603
container_title Proceedings of the American Mathematical Society
container_volume 150
creator Levinson, Jake
Ullery, Brooke
description In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley–Bacharach condition. In particular, by bounding the number of points satisfying the Cayley–Bacharach condition, we force them to lie on unions of low-dimensional linear spaces. These results are motivated by investigations into degrees of irrationality of complete intersections, which are controlled by minimum-degree rational maps to projective space. As an application of our main theorem, we describe the fibers of such maps for certain complete intersections of codimension two.
doi_str_mv 10.1090/proc/15983
format Article
fullrecord <record><control><sourceid>ams_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1090_proc_15983</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1090_proc_15983</sourcerecordid><originalsourceid>FETCH-LOGICAL-a261t-8b056fd9386e2d7a79fde5da94f0efaff1844c04f6fd731a694bacfc5bd82b83</originalsourceid><addsrcrecordid>eNp9j01LxDAURYMoWEc3_oJu3AhxXto0TZZjcVQYcDP78prkOZV-kYyL_ns7jms393LhcOEwdi_gSYCB9RRGuxaF0fkFSwRozZXO1CVLACDjxuTmmt3E-LVMYWSZMLlJK5w7P3P-jPaAYYn0ePBj8H2Kg0unDgef2nGg9vM74LEdh3jLrgi76O_-esX225d99cZ3H6_v1WbHMVPiyHUDhSJncq185kosDTlfODSSwBMSCS2lBUkLVOYClZENWrJF43TW6HzFHs-3NowxBk_1FNoew1wLqE-69Um3_tVd4IczjH38j_sBfMNVVw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Cayley--Bacharach theorem and plane configurations</title><source>American Mathematical Society Publications</source><creator>Levinson, Jake ; Ullery, Brooke</creator><creatorcontrib>Levinson, Jake ; Ullery, Brooke</creatorcontrib><description>In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley–Bacharach condition. In particular, by bounding the number of points satisfying the Cayley–Bacharach condition, we force them to lie on unions of low-dimensional linear spaces. These results are motivated by investigations into degrees of irrationality of complete intersections, which are controlled by minimum-degree rational maps to projective space. As an application of our main theorem, we describe the fibers of such maps for certain complete intersections of codimension two.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/proc/15983</identifier><language>eng</language><ispartof>Proceedings of the American Mathematical Society, 2022-11, Vol.150 (11), p.4603-4618</ispartof><rights>Copyright 2022, American Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a261t-8b056fd9386e2d7a79fde5da94f0efaff1844c04f6fd731a694bacfc5bd82b83</citedby><cites>FETCH-LOGICAL-a261t-8b056fd9386e2d7a79fde5da94f0efaff1844c04f6fd731a694bacfc5bd82b83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ams.org/proc/2022-150-11/S0002-9939-2022-15983-8/S0002-9939-2022-15983-8.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttps://www.ams.org/proc/2022-150-11/S0002-9939-2022-15983-8/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>68,314,780,784,23328,27924,27925,77836,77846</link.rule.ids></links><search><creatorcontrib>Levinson, Jake</creatorcontrib><creatorcontrib>Ullery, Brooke</creatorcontrib><title>A Cayley--Bacharach theorem and plane configurations</title><title>Proceedings of the American Mathematical Society</title><description>In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley–Bacharach condition. In particular, by bounding the number of points satisfying the Cayley–Bacharach condition, we force them to lie on unions of low-dimensional linear spaces. These results are motivated by investigations into degrees of irrationality of complete intersections, which are controlled by minimum-degree rational maps to projective space. As an application of our main theorem, we describe the fibers of such maps for certain complete intersections of codimension two.</description><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9j01LxDAURYMoWEc3_oJu3AhxXto0TZZjcVQYcDP78prkOZV-kYyL_ns7jms393LhcOEwdi_gSYCB9RRGuxaF0fkFSwRozZXO1CVLACDjxuTmmt3E-LVMYWSZMLlJK5w7P3P-jPaAYYn0ePBj8H2Kg0unDgef2nGg9vM74LEdh3jLrgi76O_-esX225d99cZ3H6_v1WbHMVPiyHUDhSJncq185kosDTlfODSSwBMSCS2lBUkLVOYClZENWrJF43TW6HzFHs-3NowxBk_1FNoew1wLqE-69Um3_tVd4IczjH38j_sBfMNVVw</recordid><startdate>20221101</startdate><enddate>20221101</enddate><creator>Levinson, Jake</creator><creator>Ullery, Brooke</creator><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20221101</creationdate><title>A Cayley--Bacharach theorem and plane configurations</title><author>Levinson, Jake ; Ullery, Brooke</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a261t-8b056fd9386e2d7a79fde5da94f0efaff1844c04f6fd731a694bacfc5bd82b83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Levinson, Jake</creatorcontrib><creatorcontrib>Ullery, Brooke</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>Levinson, Jake</au><au>Ullery, Brooke</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Cayley--Bacharach theorem and plane configurations</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2022-11-01</date><risdate>2022</risdate><volume>150</volume><issue>11</issue><spage>4603</spage><epage>4618</epage><pages>4603-4618</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><abstract>In this paper, we examine linear conditions on finite sets of points in projective space implied by the Cayley–Bacharach condition. In particular, by bounding the number of points satisfying the Cayley–Bacharach condition, we force them to lie on unions of low-dimensional linear spaces. These results are motivated by investigations into degrees of irrationality of complete intersections, which are controlled by minimum-degree rational maps to projective space. As an application of our main theorem, we describe the fibers of such maps for certain complete intersections of codimension two.</abstract><doi>10.1090/proc/15983</doi><tpages>16</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0002-9939
ispartof Proceedings of the American Mathematical Society, 2022-11, Vol.150 (11), p.4603-4618
issn 0002-9939
1088-6826
language eng
recordid cdi_crossref_primary_10_1090_proc_15983
source American Mathematical Society Publications
title A Cayley--Bacharach theorem and plane configurations
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T18%3A58%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-ams_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Cayley--Bacharach%20theorem%20and%20plane%20configurations&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.au=Levinson,%20Jake&rft.date=2022-11-01&rft.volume=150&rft.issue=11&rft.spage=4603&rft.epage=4618&rft.pages=4603-4618&rft.issn=0002-9939&rft.eissn=1088-6826&rft_id=info:doi/10.1090/proc/15983&rft_dat=%3Cams_cross%3E10_1090_proc_15983%3C/ams_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/&rfr_iscdi=true