Local vanishing for toric varieties
Let \(X\) be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves \(R^if_*\Omega^p_{\tilde X}(\log E)\), where \(f: \tilde{X} \to X\) is a strong log resolution of singularities with reduced exceptional divisor \(E\). These extend the local vanishing theorem for toric...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2024-04 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Shen, Wanchun Venkatesh, Sridhar Vo, Anh Duc |
| description | Let \(X\) be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves \(R^if_*\Omega^p_{\tilde X}(\log E)\), where \(f: \tilde{X} \to X\) is a strong log resolution of singularities with reduced exceptional divisor \(E\). These extend the local vanishing theorem for toric varieties in [MOP20]. Our consideration of these sheaves is motivated by the notion of \(k\)-rational singularities introduced by Friedman and Laza [FL22b]. In particular, our results lead to criteria for toric varieties to have \(k\)-rational singularities, as defined in [SVV23]. |
| doi_str_mv | 10.48550/arxiv.2306.10179 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_2306_10179</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2828072596</sourcerecordid><originalsourceid>FETCH-LOGICAL-a959-4366f624cc6ab36a3db02472a90a853618744440c59e799df9980194570862823</originalsourceid><addsrcrecordid>eNotj01rwkAYhJdCoWL9AT0Z8Jz03Xc_32ORfkGgF-_LGhO7YhO7G6X9992qcxkYhmEexh44VNIqBY8-_oRThQJ0xYEbumETFIKXViLesVlKOwBAbVApMWGLemj8vjj5PqTP0G-LbojFOMTQ5CyGdgxtume3nd-ndnb1KVu9PK-Wb2X98fq-fKpLT4pKKbTuNMqm0X4ttBebNaA06Am8VUJza2QWNIpaQ7TpiCxwksqA1WhRTNn8MnsmcIcYvnz8df8k7kySG4tL4xCH72ObRrcbjrHPn1wesJCZSIs_fK1IOA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2828072596</pqid></control><display><type>article</type><title>Local vanishing for toric varieties</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Shen, Wanchun ; Venkatesh, Sridhar ; Vo, Anh Duc</creator><creatorcontrib>Shen, Wanchun ; Venkatesh, Sridhar ; Vo, Anh Duc</creatorcontrib><description>Let \(X\) be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves \(R^if_*\Omega^p_{\tilde X}(\log E)\), where \(f: \tilde{X} \to X\) is a strong log resolution of singularities with reduced exceptional divisor \(E\). These extend the local vanishing theorem for toric varieties in [MOP20]. Our consideration of these sheaves is motivated by the notion of \(k\)-rational singularities introduced by Friedman and Laza [FL22b]. In particular, our results lead to criteria for toric varieties to have \(k\)-rational singularities, as defined in [SVV23].</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.2306.10179</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Mathematics - Algebraic Geometry ; Mathematics - Commutative Algebra ; Sheaves ; Singularities</subject><ispartof>arXiv.org, 2024-04</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,780,881,27904</link.rule.ids><backlink>$$Uhttps://doi.org/10.1007/s00229-024-01553-3$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2306.10179$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Shen, Wanchun</creatorcontrib><creatorcontrib>Venkatesh, Sridhar</creatorcontrib><creatorcontrib>Vo, Anh Duc</creatorcontrib><title>Local vanishing for toric varieties</title><title>arXiv.org</title><description>Let \(X\) be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves \(R^if_*\Omega^p_{\tilde X}(\log E)\), where \(f: \tilde{X} \to X\) is a strong log resolution of singularities with reduced exceptional divisor \(E\). These extend the local vanishing theorem for toric varieties in [MOP20]. Our consideration of these sheaves is motivated by the notion of \(k\)-rational singularities introduced by Friedman and Laza [FL22b]. In particular, our results lead to criteria for toric varieties to have \(k\)-rational singularities, as defined in [SVV23].</description><subject>Mathematics - Algebraic Geometry</subject><subject>Mathematics - Commutative Algebra</subject><subject>Sheaves</subject><subject>Singularities</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj01rwkAYhJdCoWL9AT0Z8Jz03Xc_32ORfkGgF-_LGhO7YhO7G6X9992qcxkYhmEexh44VNIqBY8-_oRThQJ0xYEbumETFIKXViLesVlKOwBAbVApMWGLemj8vjj5PqTP0G-LbojFOMTQ5CyGdgxtume3nd-ndnb1KVu9PK-Wb2X98fq-fKpLT4pKKbTuNMqm0X4ttBebNaA06Am8VUJza2QWNIpaQ7TpiCxwksqA1WhRTNn8MnsmcIcYvnz8df8k7kySG4tL4xCH72ObRrcbjrHPn1wesJCZSIs_fK1IOA</recordid><startdate>20240429</startdate><enddate>20240429</enddate><creator>Shen, Wanchun</creator><creator>Venkatesh, Sridhar</creator><creator>Vo, Anh Duc</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><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240429</creationdate><title>Local vanishing for toric varieties</title><author>Shen, Wanchun ; Venkatesh, Sridhar ; Vo, Anh Duc</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a959-4366f624cc6ab36a3db02472a90a853618744440c59e799df9980194570862823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Algebraic Geometry</topic><topic>Mathematics - Commutative Algebra</topic><topic>Sheaves</topic><topic>Singularities</topic><toplevel>online_resources</toplevel><creatorcontrib>Shen, Wanchun</creatorcontrib><creatorcontrib>Venkatesh, Sridhar</creatorcontrib><creatorcontrib>Vo, Anh Duc</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</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 Database</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><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shen, Wanchun</au><au>Venkatesh, Sridhar</au><au>Vo, Anh Duc</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Local vanishing for toric varieties</atitle><jtitle>arXiv.org</jtitle><date>2024-04-29</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>Let \(X\) be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves \(R^if_*\Omega^p_{\tilde X}(\log E)\), where \(f: \tilde{X} \to X\) is a strong log resolution of singularities with reduced exceptional divisor \(E\). These extend the local vanishing theorem for toric varieties in [MOP20]. Our consideration of these sheaves is motivated by the notion of \(k\)-rational singularities introduced by Friedman and Laza [FL22b]. In particular, our results lead to criteria for toric varieties to have \(k\)-rational singularities, as defined in [SVV23].</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.2306.10179</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2024-04 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_2306_10179 |
| source | arXiv.org; Free E- Journals |
| subjects | Mathematics - Algebraic Geometry Mathematics - Commutative Algebra Sheaves Singularities |
| title | Local vanishing for toric varieties |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-21T19%3A23%3A39IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Local%20vanishing%20for%20toric%20varieties&rft.jtitle=arXiv.org&rft.au=Shen,%20Wanchun&rft.date=2024-04-29&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.2306.10179&rft_dat=%3Cproquest_arxiv%3E2828072596%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2828072596&rft_id=info:pmid/&rfr_iscdi=true |