Polar Multiplicities and Integral Dependence

Abstract We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is a reduction of another in terms of certain mixed B...

Full description

Saved in:
Bibliographic Details
Published in:International mathematics research notices 2024-09, Vol.2024 (17), p.12201-12218
Main Author: Cid-Ruiz, Yairon
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c192t-fff309785a2c3a3e270dfcb9c5c7f2d8373b6d03c8ef27fad8eaa3e7697077e23
container_end_page 12218
container_issue 17
container_start_page 12201
container_title International mathematics research notices
container_volume 2024
creator Cid-Ruiz, Yairon
description Abstract We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is a reduction of another in terms of certain mixed Buchsbaum–Rim multiplicities. Furthermore, we prove several technical results regarding polar multiplicities.
doi_str_mv 10.1093/imrn/rnae163
format article
fullrecord <record><control><sourceid>oup_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1093_imrn_rnae163</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><oup_id>10.1093/imrn/rnae163</oup_id><sourcerecordid>10.1093/imrn/rnae163</sourcerecordid><originalsourceid>FETCH-LOGICAL-c192t-fff309785a2c3a3e270dfcb9c5c7f2d8373b6d03c8ef27fad8eaa3e7697077e23</originalsourceid><addsrcrecordid>eNp9zzFPwzAQhmELgUQpbPyAbCw1Pds0Z4-oUKhUBAPMkWufkVHqRHY68O9J1c5Md8OjT3oZuxVwL8CoedzlNM_JkqjVGZuIWiMH-YDn4w-oOBqpL9lVKT8AEoRWEzb76Fqbq7d9O8S-jS4OkUplk6_WaaDvbNvqiXpKnpKja3YRbFvo5nSn7Gv1_Ll85Zv3l_XyccOdMHLgIQQFBvXCSqesIongg9sat3AYpNcK1bb2oJymIDFYr8mODGuDgEhSTdnsuOtyV0qm0PQ57mz-bQQ0h9LmUNqcSkd-d-Tdvv9f_gHM2VZa</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Polar Multiplicities and Integral Dependence</title><source>Oxford Journals Online</source><creator>Cid-Ruiz, Yairon</creator><creatorcontrib>Cid-Ruiz, Yairon</creatorcontrib><description>Abstract We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is a reduction of another in terms of certain mixed Buchsbaum–Rim multiplicities. Furthermore, we prove several technical results regarding polar multiplicities.</description><identifier>ISSN: 1073-7928</identifier><identifier>EISSN: 1687-0247</identifier><identifier>DOI: 10.1093/imrn/rnae163</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>International mathematics research notices, 2024-09, Vol.2024 (17), p.12201-12218</ispartof><rights>The Author(s) 2024. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com. 2024</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c192t-fff309785a2c3a3e270dfcb9c5c7f2d8373b6d03c8ef27fad8eaa3e7697077e23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Cid-Ruiz, Yairon</creatorcontrib><title>Polar Multiplicities and Integral Dependence</title><title>International mathematics research notices</title><description>Abstract We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is a reduction of another in terms of certain mixed Buchsbaum–Rim multiplicities. Furthermore, we prove several technical results regarding polar multiplicities.</description><issn>1073-7928</issn><issn>1687-0247</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>TOX</sourceid><recordid>eNp9zzFPwzAQhmELgUQpbPyAbCw1Pds0Z4-oUKhUBAPMkWufkVHqRHY68O9J1c5Md8OjT3oZuxVwL8CoedzlNM_JkqjVGZuIWiMH-YDn4w-oOBqpL9lVKT8AEoRWEzb76Fqbq7d9O8S-jS4OkUplk6_WaaDvbNvqiXpKnpKja3YRbFvo5nSn7Gv1_Ll85Zv3l_XyccOdMHLgIQQFBvXCSqesIongg9sat3AYpNcK1bb2oJymIDFYr8mODGuDgEhSTdnsuOtyV0qm0PQ57mz-bQQ0h9LmUNqcSkd-d-Tdvv9f_gHM2VZa</recordid><startdate>20240909</startdate><enddate>20240909</enddate><creator>Cid-Ruiz, Yairon</creator><general>Oxford University Press</general><scope>TOX</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20240909</creationdate><title>Polar Multiplicities and Integral Dependence</title><author>Cid-Ruiz, Yairon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c192t-fff309785a2c3a3e270dfcb9c5c7f2d8373b6d03c8ef27fad8eaa3e7697077e23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cid-Ruiz, Yairon</creatorcontrib><collection>Open Access: Oxford University Press Open Journals</collection><collection>CrossRef</collection><jtitle>International mathematics research notices</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Cid-Ruiz, Yairon</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polar Multiplicities and Integral Dependence</atitle><jtitle>International mathematics research notices</jtitle><date>2024-09-09</date><risdate>2024</risdate><volume>2024</volume><issue>17</issue><spage>12201</spage><epage>12218</epage><pages>12201-12218</pages><issn>1073-7928</issn><eissn>1687-0247</eissn><abstract>Abstract We provide new criteria for the integrality and birationality of an extension of graded algebras in terms of the general notion of polar multiplicities of Kleiman and Thorup. As an application, we obtain a new criterion for when a module is a reduction of another in terms of certain mixed Buchsbaum–Rim multiplicities. Furthermore, we prove several technical results regarding polar multiplicities.</abstract><pub>Oxford University Press</pub><doi>10.1093/imrn/rnae163</doi><tpages>18</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1073-7928
ispartof International mathematics research notices, 2024-09, Vol.2024 (17), p.12201-12218
issn 1073-7928
1687-0247
language eng
recordid cdi_crossref_primary_10_1093_imrn_rnae163
source Oxford Journals Online
title Polar Multiplicities and Integral Dependence
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T12%3A45%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-oup_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Polar%20Multiplicities%20and%20Integral%20Dependence&rft.jtitle=International%20mathematics%20research%20notices&rft.au=Cid-Ruiz,%20Yairon&rft.date=2024-09-09&rft.volume=2024&rft.issue=17&rft.spage=12201&rft.epage=12218&rft.pages=12201-12218&rft.issn=1073-7928&rft.eissn=1687-0247&rft_id=info:doi/10.1093/imrn/rnae163&rft_dat=%3Coup_cross%3E10.1093/imrn/rnae163%3C/oup_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c192t-fff309785a2c3a3e270dfcb9c5c7f2d8373b6d03c8ef27fad8eaa3e7697077e23%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_oup_id=10.1093/imrn/rnae163&rfr_iscdi=true