Stable Ulrich bundles on cubic fourfolds

In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, dep...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-06
Main Authors: Hoang Le Truong, Yen, Hoang Ngoc
Format: Article
Language:English
Subjects:
Mathematical analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Hoang Le Truong
Yen, Hoang Ngoc
description In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, depending roughly on \(r\) parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new \(19\)-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold \(X\), there exist arithmetically Cohen-Macaulay smooth surface \(Y \subset X\) which are not an intersection \(X \cap T\) for a codimension two subvariety \(T \subset \Bbb P^5\).
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2676380536</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2676380536</sourcerecordid><originalsourceid>FETCH-proquest_journals_26763805363</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQCC5JTMpJVQjNKcpMzlBIKs1LyUktVsjPU0guTcpMVkjLLy1Ky89JKeZhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWUCleUCpeKDhZsYWBqbGZsbEqQIAmN0wDw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2676380536</pqid></control><display><type>article</type><title>Stable Ulrich bundles on cubic fourfolds</title><source>Publicly Available Content (ProQuest)</source><creator>Hoang Le Truong ; Yen, Hoang Ngoc</creator><creatorcontrib>Hoang Le Truong ; Yen, Hoang Ngoc</creatorcontrib><description>In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, depending roughly on \(r\) parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new \(19\)-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold \(X\), there exist arithmetically Cohen-Macaulay smooth surface \(Y \subset X\) which are not an intersection \(X \cap T\) for a codimension two subvariety \(T \subset \Bbb P^5\).</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Mathematical analysis</subject><ispartof>arXiv.org, 2022-06</ispartof><rights>2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2676380536?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Hoang Le Truong</creatorcontrib><creatorcontrib>Yen, Hoang Ngoc</creatorcontrib><title>Stable Ulrich bundles on cubic fourfolds</title><title>arXiv.org</title><description>In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, depending roughly on \(r\) parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new \(19\)-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold \(X\), there exist arithmetically Cohen-Macaulay smooth surface \(Y \subset X\) which are not an intersection \(X \cap T\) for a codimension two subvariety \(T \subset \Bbb P^5\).</description><subject>Mathematical analysis</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQCC5JTMpJVQjNKcpMzlBIKs1LyUktVsjPU0guTcpMVkjLLy1Ky89JKeZhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWUCleUCpeKDhZsYWBqbGZsbEqQIAmN0wDw</recordid><startdate>20220610</startdate><enddate>20220610</enddate><creator>Hoang Le Truong</creator><creator>Yen, Hoang Ngoc</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20220610</creationdate><title>Stable Ulrich bundles on cubic fourfolds</title><author>Hoang Le Truong ; Yen, Hoang Ngoc</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_26763805363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematical analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Hoang Le Truong</creatorcontrib><creatorcontrib>Yen, Hoang Ngoc</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hoang Le Truong</au><au>Yen, Hoang Ngoc</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Stable Ulrich bundles on cubic fourfolds</atitle><jtitle>arXiv.org</jtitle><date>2022-06-10</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold \(X\) of given rank \(r\). As consequences, we show that for every integer \(r\ge 2\) there exists a family of indecomposable rank \(r\) Ulrich bundles on the certain cubic fourfolds, depending roughly on \(r\) parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new \(19\)-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold \(X\), there exist arithmetically Cohen-Macaulay smooth surface \(Y \subset X\) which are not an intersection \(X \cap T\) for a codimension two subvariety \(T \subset \Bbb P^5\).</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2022-06
issn 2331-8422
language eng
recordid cdi_proquest_journals_2676380536
source Publicly Available Content (ProQuest)
subjects Mathematical analysis
title Stable Ulrich bundles on cubic fourfolds
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T01%3A35%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Stable%20Ulrich%20bundles%20on%20cubic%20fourfolds&rft.jtitle=arXiv.org&rft.au=Hoang%20Le%20Truong&rft.date=2022-06-10&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2676380536%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_26763805363%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2676380536&rft_id=info:pmid/&rfr_iscdi=true