Functorial destackification of tame stacks with abelian stabilisers
We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. A...
Gespeichert in:
| Veröffentlicht in: | Compositio mathematica 2017-06, Vol.153 (6), p.1257-1315 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1315 |
|---|---|
| container_issue | 6 |
| container_start_page | 1257 |
| container_title | Compositio mathematica |
| container_volume | 153 |
| creator | Bergh, Daniel |
| description | We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic
$0$
, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties with simplicial toric quotient singularities, without assuming the presence of a toroidal structure. |
| doi_str_mv | 10.1112/S0010437X17007084 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2356723159</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1112_S0010437X17007084</cupid><sourcerecordid>2356723159</sourcerecordid><originalsourceid>FETCH-LOGICAL-c360t-13c9a82f56b41f968574f42c7639e94dc5b875843559c85e63b69c93858a5c633</originalsourceid><addsrcrecordid>eNp1UMtKxDAUDaLgOPoB7gquqzfvZCnFUWHAhQruSpommrGPMWkR_97WGXAhri6c1z0chM4xXGKMydUjAAZG5QuWABIUO0ALzCXkXDFxiBYznc_8MTpJaQMARBG1QMVq7OzQx2CarHZpMPY9-GDNEPou6302mNZlP3DKPsPwlpnKNcF0M1aFJiQX0yk68qZJ7mx_l-h5dfNU3OXrh9v74nqdWypgyDG12ijiuagY9looLplnxEpBtdOstrxScqpLOddWcSdoJbTVVHFluBWULtHFLncb-49xKltu-jF208uSUC4koZjrSYV3Khv7lKLz5TaG1sSvEkM5b1X-2Wry0L3HtFUM9av7jf7f9Q2F-mo_</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2356723159</pqid></control><display><type>article</type><title>Functorial destackification of tame stacks with abelian stabilisers</title><source>EZB-FREE-00999 freely available EZB journals</source><source>Cambridge University Press Journals Complete</source><creator>Bergh, Daniel</creator><creatorcontrib>Bergh, Daniel</creatorcontrib><description>We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic
$0$
, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties with simplicial toric quotient singularities, without assuming the presence of a toroidal structure.</description><identifier>ISSN: 0010-437X</identifier><identifier>EISSN: 1570-5846</identifier><identifier>DOI: 10.1112/S0010437X17007084</identifier><language>eng</language><publisher>London, UK: London Mathematical Society</publisher><ispartof>Compositio mathematica, 2017-06, Vol.153 (6), p.1257-1315</ispartof><rights>The Author 2017</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-13c9a82f56b41f968574f42c7639e94dc5b875843559c85e63b69c93858a5c633</citedby><cites>FETCH-LOGICAL-c360t-13c9a82f56b41f968574f42c7639e94dc5b875843559c85e63b69c93858a5c633</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0010437X17007084/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids></links><search><creatorcontrib>Bergh, Daniel</creatorcontrib><title>Functorial destackification of tame stacks with abelian stabilisers</title><title>Compositio mathematica</title><addtitle>Compositio Math</addtitle><description>We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic
$0$
, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties with simplicial toric quotient singularities, without assuming the presence of a toroidal structure.</description><issn>0010-437X</issn><issn>1570-5846</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1UMtKxDAUDaLgOPoB7gquqzfvZCnFUWHAhQruSpommrGPMWkR_97WGXAhri6c1z0chM4xXGKMydUjAAZG5QuWABIUO0ALzCXkXDFxiBYznc_8MTpJaQMARBG1QMVq7OzQx2CarHZpMPY9-GDNEPou6302mNZlP3DKPsPwlpnKNcF0M1aFJiQX0yk68qZJ7mx_l-h5dfNU3OXrh9v74nqdWypgyDG12ijiuagY9looLplnxEpBtdOstrxScqpLOddWcSdoJbTVVHFluBWULtHFLncb-49xKltu-jF208uSUC4koZjrSYV3Khv7lKLz5TaG1sSvEkM5b1X-2Wry0L3HtFUM9av7jf7f9Q2F-mo_</recordid><startdate>201706</startdate><enddate>201706</enddate><creator>Bergh, Daniel</creator><general>London Mathematical Society</general><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7XB</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>201706</creationdate><title>Functorial destackification of tame stacks with abelian stabilisers</title><author>Bergh, Daniel</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-13c9a82f56b41f968574f42c7639e94dc5b875843559c85e63b69c93858a5c633</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bergh, Daniel</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</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>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</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>ProQuest Central Basic</collection><jtitle>Compositio mathematica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bergh, Daniel</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Functorial destackification of tame stacks with abelian stabilisers</atitle><jtitle>Compositio mathematica</jtitle><addtitle>Compositio Math</addtitle><date>2017-06</date><risdate>2017</risdate><volume>153</volume><issue>6</issue><spage>1257</spage><epage>1315</epage><pages>1257-1315</pages><issn>0010-437X</issn><eissn>1570-5846</eissn><abstract>We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic
$0$
, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties with simplicial toric quotient singularities, without assuming the presence of a toroidal structure.</abstract><cop>London, UK</cop><pub>London Mathematical Society</pub><doi>10.1112/S0010437X17007084</doi><tpages>59</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0010-437X |
| ispartof | Compositio mathematica, 2017-06, Vol.153 (6), p.1257-1315 |
| issn | 0010-437X 1570-5846 |
| language | eng |
| recordid | cdi_proquest_journals_2356723159 |
| source | EZB-FREE-00999 freely available EZB journals; Cambridge University Press Journals Complete |
| title | Functorial destackification of tame stacks with abelian stabilisers |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T11%3A28%3A49IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Functorial%20destackification%20of%20tame%20stacks%20with%20abelian%20stabilisers&rft.jtitle=Compositio%20mathematica&rft.au=Bergh,%20Daniel&rft.date=2017-06&rft.volume=153&rft.issue=6&rft.spage=1257&rft.epage=1315&rft.pages=1257-1315&rft.issn=0010-437X&rft.eissn=1570-5846&rft_id=info:doi/10.1112/S0010437X17007084&rft_dat=%3Cproquest_cross%3E2356723159%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2356723159&rft_id=info:pmid/&rft_cupid=10_1112_S0010437X17007084&rfr_iscdi=true |