Ulrich bundles on cubic fourfolds

Ulrich bundles on cubic fourfolds

We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf \mathcal E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an \mathcal E appears as an extension of two Lehn–Lehn–Sorger–van Straten sheav...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Commentarii mathematici Helvetici 2022-01, Vol.97 (4), p.691-728
Hauptverfasser: Faenzi, Daniele, Kim, Yeongrak
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 728
container_issue 4
container_start_page 691
container_title Commentarii mathematici Helvetici
container_volume 97
creator Faenzi, Daniele
Kim, Yeongrak
description We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf \mathcal E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an \mathcal E appears as an extension of two Lehn–Lehn–Sorger–van Straten sheaves. Then we prove that a general deformation of \mathcal E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.
doi_str_mv 10.4171/cmh/546
format Article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_03951392v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_03951392v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c330t-64bd2c75c55dc7cf60f0301725eef229fb72ab88658d54fc5c755ef024a3b2013</originalsourceid><addsrcrecordid>eNo9kMFKxDAURYMoWEfxF-pKXNR5L8lr2uUwqCMU3DjrkKQJrXSmkljBv7dlxNWFy7l3cRi7RXiUqHDtDt2aZHnGMpQciqqW5TnLABAKTgov2VVKHwBQKYUZu9sPsXddbqdjO_iUj8fcTbZ3eRinGMahTdfsIpgh-Zu_XLH989P7dlc0by-v201TOCHgqyilbblT5Ihap1woIYAAVJy8D5zXwSpubFWVVLUkg6OZJR-ASyMsBxQr9nD67cygP2N_MPFHj6bXu02jlw5ETShq_r2w9yfWxTGl6MP_AEEvFvRsQc8WxC-f8k1L</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Ulrich bundles on cubic fourfolds</title><source>DOAJ Directory of Open Access Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>European Mathematical Society Publishing House</source><creator>Faenzi, Daniele ; Kim, Yeongrak</creator><creatorcontrib>Faenzi, Daniele ; Kim, Yeongrak</creatorcontrib><description>We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf \mathcal E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an \mathcal E appears as an extension of two Lehn–Lehn–Sorger–van Straten sheaves. Then we prove that a general deformation of \mathcal E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.</description><identifier>ISSN: 0010-2571</identifier><identifier>EISSN: 1420-8946</identifier><identifier>DOI: 10.4171/cmh/546</identifier><language>eng</language><publisher>European Mathematical Society</publisher><subject>Mathematics</subject><ispartof>Commentarii mathematici Helvetici, 2022-01, Vol.97 (4), p.691-728</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c330t-64bd2c75c55dc7cf60f0301725eef229fb72ab88658d54fc5c755ef024a3b2013</citedby><orcidid>0000-0002-4411-0952</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,777,781,861,882,27905,27906</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03951392$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Faenzi, Daniele</creatorcontrib><creatorcontrib>Kim, Yeongrak</creatorcontrib><title>Ulrich bundles on cubic fourfolds</title><title>Commentarii mathematici Helvetici</title><description>We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf \mathcal E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an \mathcal E appears as an extension of two Lehn–Lehn–Sorger–van Straten sheaves. Then we prove that a general deformation of \mathcal E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.</description><subject>Mathematics</subject><issn>0010-2571</issn><issn>1420-8946</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNo9kMFKxDAURYMoWEfxF-pKXNR5L8lr2uUwqCMU3DjrkKQJrXSmkljBv7dlxNWFy7l3cRi7RXiUqHDtDt2aZHnGMpQciqqW5TnLABAKTgov2VVKHwBQKYUZu9sPsXddbqdjO_iUj8fcTbZ3eRinGMahTdfsIpgh-Zu_XLH989P7dlc0by-v201TOCHgqyilbblT5Ihap1woIYAAVJy8D5zXwSpubFWVVLUkg6OZJR-ASyMsBxQr9nD67cygP2N_MPFHj6bXu02jlw5ETShq_r2w9yfWxTGl6MP_AEEvFvRsQc8WxC-f8k1L</recordid><startdate>20220101</startdate><enddate>20220101</enddate><creator>Faenzi, Daniele</creator><creator>Kim, Yeongrak</creator><general>European Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-4411-0952</orcidid></search><sort><creationdate>20220101</creationdate><title>Ulrich bundles on cubic fourfolds</title><author>Faenzi, Daniele ; Kim, Yeongrak</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c330t-64bd2c75c55dc7cf60f0301725eef229fb72ab88658d54fc5c755ef024a3b2013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Faenzi, Daniele</creatorcontrib><creatorcontrib>Kim, Yeongrak</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Commentarii mathematici Helvetici</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Faenzi, Daniele</au><au>Kim, Yeongrak</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ulrich bundles on cubic fourfolds</atitle><jtitle>Commentarii mathematici Helvetici</jtitle><date>2022-01-01</date><risdate>2022</risdate><volume>97</volume><issue>4</issue><spage>691</spage><epage>728</epage><pages>691-728</pages><issn>0010-2571</issn><eissn>1420-8946</eissn><abstract>We show the existence of rank 6 Ulrich bundles on a smooth cubic fourfold. First, we construct a simple sheaf \mathcal E of rank 6 as an elementary modification of an ACM bundle of rank 6 on a smooth cubic fourfold. Such an \mathcal E appears as an extension of two Lehn–Lehn–Sorger–van Straten sheaves. Then we prove that a general deformation of \mathcal E(1) becomes Ulrich. In particular, this says that general cubic fourfolds have Ulrich complexity 6.</abstract><pub>European Mathematical Society</pub><doi>10.4171/cmh/546</doi><tpages>38</tpages><orcidid>https://orcid.org/0000-0002-4411-0952</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0010-2571
ispartof Commentarii mathematici Helvetici, 2022-01, Vol.97 (4), p.691-728
issn 0010-2571
1420-8946
language eng
recordid cdi_hal_primary_oai_HAL_hal_03951392v1
source DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; European Mathematical Society Publishing House
subjects Mathematics
title Ulrich bundles on cubic fourfolds
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T03%3A36%3A08IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Ulrich%20bundles%20on%20cubic%20fourfolds&rft.jtitle=Commentarii%20mathematici%20Helvetici&rft.au=Faenzi,%20Daniele&rft.date=2022-01-01&rft.volume=97&rft.issue=4&rft.spage=691&rft.epage=728&rft.pages=691-728&rft.issn=0010-2571&rft.eissn=1420-8946&rft_id=info:doi/10.4171/cmh/546&rft_dat=%3Chal_cross%3Eoai_HAL_hal_03951392v1%3C/hal_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