Maximal minors and linear powers
An ideal in a polynomial ring has linear powers if all the powers of have a linear free resolution. We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers. The required genericity is expressed in terms of the heights of the ideals of lower ord...
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| Veröffentlicht in: | Journal für die reine und angewandte Mathematik 2015-05, Vol.2015 (702), p.41-53 |
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| container_end_page | 53 |
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| container_issue | 702 |
| container_start_page | 41 |
| container_title | Journal für die reine und angewandte Mathematik |
| container_volume | 2015 |
| creator | Bruns, Winfried Conca, Aldo Varbaro, Matteo |
| description | An ideal
in a polynomial ring
has linear powers if all the powers
of
have a linear free resolution.
We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers.
The required genericity is expressed in terms of the heights of the ideals of lower order minors.
In particular we prove that every rational normal scroll has linear powers. |
| doi_str_mv | 10.1515/crelle-2013-0026 |
| format | Article |
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in a polynomial ring
has linear powers if all the powers
of
have a linear free resolution.
We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers.
The required genericity is expressed in terms of the heights of the ideals of lower order minors.
In particular we prove that every rational normal scroll has linear powers.</description><identifier>ISSN: 0075-4102</identifier><identifier>EISSN: 1435-5345</identifier><identifier>DOI: 10.1515/crelle-2013-0026</identifier><language>eng</language><publisher>De Gruyter</publisher><ispartof>Journal für die reine und angewandte Mathematik, 2015-05, Vol.2015 (702), p.41-53</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c301t-5cb8a0746ce24a8b4a2e673e50d2cabcc6863764267d0dac3d618d0b1c8cc0183</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.degruyter.com/document/doi/10.1515/crelle-2013-0026/pdf$$EPDF$$P50$$Gwalterdegruyter$$H</linktopdf><linktohtml>$$Uhttps://www.degruyter.com/document/doi/10.1515/crelle-2013-0026/html$$EHTML$$P50$$Gwalterdegruyter$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,66497,68281</link.rule.ids></links><search><creatorcontrib>Bruns, Winfried</creatorcontrib><creatorcontrib>Conca, Aldo</creatorcontrib><creatorcontrib>Varbaro, Matteo</creatorcontrib><title>Maximal minors and linear powers</title><title>Journal für die reine und angewandte Mathematik</title><description>An ideal
in a polynomial ring
has linear powers if all the powers
of
have a linear free resolution.
We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers.
The required genericity is expressed in terms of the heights of the ideals of lower order minors.
In particular we prove that every rational normal scroll has linear powers.</description><issn>0075-4102</issn><issn>1435-5345</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp1j8tOwzAURC0EEqGwZ5kfMNzr97aqeElFbGBtOdcuSpUmld2q9O9JFLasZjZnNIexe4QH1KgfKaeuS1wASg4gzAWrUEnNtVT6klUAVnOFIK7ZTSlbANBoRcXq9_DT7kJX79p-yKUOfay7tk8h1_vhlHK5ZVeb0JV095cL9vX89Ll65euPl7fVcs1JAh64psYFsMpQEiq4RgWRjJVJQxQUGiLjjLRGCWMjxEAyGnQRGiRHBOjkgsG8S3koJaeN3-fxWD57BD8Z-tnQT4Z-MhyR5YycQndIOabvfDyPxW-HY-7Hs_-iY9EWhEL5CybzWaw</recordid><startdate>20150501</startdate><enddate>20150501</enddate><creator>Bruns, Winfried</creator><creator>Conca, Aldo</creator><creator>Varbaro, Matteo</creator><general>De Gruyter</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20150501</creationdate><title>Maximal minors and linear powers</title><author>Bruns, Winfried ; Conca, Aldo ; Varbaro, Matteo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c301t-5cb8a0746ce24a8b4a2e673e50d2cabcc6863764267d0dac3d618d0b1c8cc0183</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bruns, Winfried</creatorcontrib><creatorcontrib>Conca, Aldo</creatorcontrib><creatorcontrib>Varbaro, Matteo</creatorcontrib><collection>CrossRef</collection><jtitle>Journal für die reine und angewandte Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bruns, Winfried</au><au>Conca, Aldo</au><au>Varbaro, Matteo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maximal minors and linear powers</atitle><jtitle>Journal für die reine und angewandte Mathematik</jtitle><date>2015-05-01</date><risdate>2015</risdate><volume>2015</volume><issue>702</issue><spage>41</spage><epage>53</epage><pages>41-53</pages><issn>0075-4102</issn><eissn>1435-5345</eissn><abstract>An ideal
in a polynomial ring
has linear powers if all the powers
of
have a linear free resolution.
We show that the ideal of maximal minors of a sufficiently general matrix with linear entries has linear powers.
The required genericity is expressed in terms of the heights of the ideals of lower order minors.
In particular we prove that every rational normal scroll has linear powers.</abstract><pub>De Gruyter</pub><doi>10.1515/crelle-2013-0026</doi><tpages>13</tpages></addata></record> |
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| identifier | ISSN: 0075-4102 |
| ispartof | Journal für die reine und angewandte Mathematik, 2015-05, Vol.2015 (702), p.41-53 |
| issn | 0075-4102 1435-5345 |
| language | eng |
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| source | De Gruyter journals |
| title | Maximal minors and linear powers |
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