{"id":"https://openalex.org/W1973486614","doi":"https://doi.org/10.1090/s0025-5718-05-01730-8","title":"Computing the tight closure in dimension two","display_name":"Computing the tight closure in dimension two","publication_year":2005,"publication_date":"2005-01-27","ids":{"openalex":"https://openalex.org/W1973486614","doi":"https://doi.org/10.1090/s0025-5718-05-01730-8","mag":"1973486614"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01730-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01730-8","pdf_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-05-01730-8/S0025-5718-05-01730-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-05-01730-8/S0025-5718-05-01730-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5076452367","display_name":"Holger Brenner","orcid":null},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Holger Brenner","raw_affiliation_strings":["Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom","Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom","institution_ids":["https://openalex.org/I91136226"]},{"raw_affiliation_string":"Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, United Kingdom#TAB#","institution_ids":["https://openalex.org/I91136226"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076452367"],"corresponding_institution_ids":["https://openalex.org/I91136226"],"apc_list":null,"apc_paid":null,"fwci":2.5245,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.87776573,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"74","issue":"251","first_page":"1495","last_page":"1518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.883743405342102},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.809073805809021},{"id":"https://openalex.org/keywords/ideal","display_name":"Ideal (ethics)","score":0.6237972378730774},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6178693771362305},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5527969598770142},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.5443148612976074},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5421465635299683},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5087974667549133},{"id":"https://openalex.org/keywords/filtration","display_name":"Filtration (mathematics)","score":0.5025455951690674},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5002701282501221},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4103946387767792},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40909814834594727},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2728523313999176},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24329254031181335},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23179841041564941},{"id":"https://openalex.org/keywords/matrix-polynomial","display_name":"Matrix polynomial","score":0.06520476937294006}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.883743405342102},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.809073805809021},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6237972378730774},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6178693771362305},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5527969598770142},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.5443148612976074},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5421465635299683},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5087974667549133},{"id":"https://openalex.org/C128489963","wikidata":"https://www.wikidata.org/wiki/Q1187724","display_name":"Filtration (mathematics)","level":2,"score":0.5025455951690674},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5002701282501221},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4103946387767792},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40909814834594727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2728523313999176},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24329254031181335},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23179841041564941},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.06520476937294006},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-05-01730-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01730-8","pdf_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-05-01730-8/S0025-5718-05-01730-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.5670","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.5670","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2005-74-251/S0025-5718-05-01730-8/S0025-5718-05-01730-8.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.7401","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.7401","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0303116v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.90","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.90","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0303116v2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01730-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01730-8","pdf_url":"https://www.ams.org/mcom/2005-74-251/S0025-5718-05-01730-8/S0025-5718-05-01730-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.6000000238418579}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973486614.pdf","grobid_xml":"https://content.openalex.org/works/W1973486614.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W47187632","https://openalex.org/W126691111","https://openalex.org/W1564169575","https://openalex.org/W1580842374","https://openalex.org/W1602877338","https://openalex.org/W1659843202","https://openalex.org/W1845187874","https://openalex.org/W1890353761","https://openalex.org/W1921466561","https://openalex.org/W1994903094","https://openalex.org/W1999376325","https://openalex.org/W2000950623","https://openalex.org/W2031241956","https://openalex.org/W2034577609","https://openalex.org/W2064026117","https://openalex.org/W2085640574","https://openalex.org/W2104302473","https://openalex.org/W2105520390","https://openalex.org/W2258062532","https://openalex.org/W2318532821","https://openalex.org/W3155258486"],"related_works":["https://openalex.org/W315394019","https://openalex.org/W2923398117","https://openalex.org/W4309585848","https://openalex.org/W2265383332","https://openalex.org/W2590472383","https://openalex.org/W4328130279","https://openalex.org/W4313657047","https://openalex.org/W3156147585","https://openalex.org/W4307350259","https://openalex.org/W2240347535"],"abstract_inverted_index":{"We":[0,19,68],"study":[1],"computational":[2],"aspects":[3],"of":[4,8,29,33,53,74],"the":[5,27,34,50,57,65,72],"tight":[6,39,51],"closure":[7,52],"a":[9,14,82,87,92,199],"homogeneous":[10,200],"primary":[11],"ideal":[12,35],"in":[13,137],"two-dimensional":[15],"normal":[16],"standard-graded":[17],"domain.":[18],"show":[20],"how":[21],"to":[22,36,48,63,71],"use":[23],"slope":[24],"criteria":[25],"for":[26,31],"sheaf":[28],"relations":[30],"generators":[32],"compute":[37,49,64],"its":[38],"closure.":[40],"In":[41],"particular,":[42],"our":[43],"method":[44],"gives":[45],"an":[46],"algorithm":[47],"three":[54],"elements":[55],"under":[56],"condition":[58],"that":[59],"we":[60],"are":[61],"able":[62],"Harder-Narasimhan":[66],"filtration.":[67],"apply":[69],"this":[70],"computation":[73],"<inline-formula":[75,138,185],"content-type=\"math/mathml\">":[76,139,186],"<mml:math":[77,140,187],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[78,141,188],"alttext=\"left-parenthesis":[79],"x":[80,145],"Superscript":[81,86,91,95],"Baseline":[83,88,93],"comma":[84,89,146,148],"y":[85,147],"z":[90,149],"right-parenthesis":[94],"asterisk\">":[96],"<mml:semantics>":[97,156,191],"<mml:mrow>":[98,157],"<mml:mo":[99,125,159,166,172,175],"stretchy=\"false\">(</mml:mo>":[100,173],"<mml:msup>":[101,109,117,124],"<mml:mi>x</mml:mi>":[102,161],"<mml:mrow":[103,111,119,168],"class=\"MJX-TeXAtom-ORD\">":[104,112,120,169],"<mml:mi>a</mml:mi>":[105,113,121],"</mml:mrow>":[106,114,122,131,171,177],"</mml:msup>":[107,115,123,130],"<mml:mo>,</mml:mo>":[108,116,162,164],"<mml:mi>y</mml:mi>":[110,163],"<mml:mi>z</mml:mi>":[118,165],"stretchy=\"false\">)</mml:mo>":[126,176],"<mml:mo>":[127],"\u2217":[128],"</mml:mo>":[129],"<mml:annotation":[132,178,193],"encoding=\"application/x-tex\">(x^{a},y^{a},z^{a})^*</mml:annotation>":[133],"</mml:semantics>":[134,180,195],"</mml:math>":[135,181,196],"</inline-formula>":[136,182,197],"alttext=\"upper":[142,189],"K":[143],"left-bracket":[144],"right-bracket":[150],"slash":[151],"left-parenthesis":[152],"upper":[153],"F":[154],"right-parenthesis\">":[155],"<mml:mi>K</mml:mi>":[158],"stretchy=\"false\">[</mml:mo>":[160],"stretchy=\"false\">]</mml:mo>":[167],"<mml:mo>/</mml:mo>":[170],"<mml:mi>F</mml:mi>":[174,192],"encoding=\"application/x-tex\">K[x,y,z]/(F)</mml:annotation>":[179],",":[183],"where":[184],"F\">":[190],"encoding=\"application/x-tex\">F</mml:annotation>":[194],"is":[198],"polynomial.":[201]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
