{"id":"https://openalex.org/W2003429475","doi":"https://doi.org/10.1112/s1461157012001040","title":"Zariski chambers on surfaces of high Picard number","display_name":"Zariski chambers on surfaces of high Picard number","publication_year":2012,"publication_date":"2012-08-01","ids":{"openalex":"https://openalex.org/W2003429475","doi":"https://doi.org/10.1112/s1461157012001040","mag":"2003429475"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157012001040","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157012001040","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2D7CD1B508808A5BA8B919F9626BDDF3/S1461157012001040a.pdf/div-class-title-zariski-chambers-on-surfaces-of-high-picard-number-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2D7CD1B508808A5BA8B919F9626BDDF3/S1461157012001040a.pdf/div-class-title-zariski-chambers-on-surfaces-of-high-picard-number-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102824468","display_name":"Thomas Bauer","orcid":"https://orcid.org/0000-0002-2426-0259"},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Thomas Bauer","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe\u00a0D-35032\u00a0Marburg, Germany","Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe, D-35032 Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe\u00a0D-35032\u00a0Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe, D-35032 Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024314063","display_name":"David Schmitz","orcid":null},"institutions":[{"id":"https://openalex.org/I161103922","display_name":"Philipps University of Marburg","ror":"https://ror.org/01rdrb571","country_code":"DE","type":"education","lineage":["https://openalex.org/I161103922"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"David Schmitz","raw_affiliation_strings":["Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe\u00a0D-35032\u00a0Marburg, Germany","Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe, D-35032 Marburg, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe\u00a0D-35032\u00a0Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]},{"raw_affiliation_string":"Fachbereich Mathematik und Informatik, Philipps-Universit\u00e4t Marburg, Hans-Meerwein-Stra\u00dfe, D-35032 Marburg, Germany","institution_ids":["https://openalex.org/I161103922"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102824468"],"corresponding_institution_ids":["https://openalex.org/I161103922"],"apc_list":null,"apc_paid":null,"fwci":1.0384,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7663799,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":null,"first_page":"219","last_page":"230"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8878565430641174},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.7927095890045166},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.672901451587677},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5119243860244751},{"id":"https://openalex.org/keywords/picard-group","display_name":"Picard group","score":0.4571913778781891},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.42141324281692505},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37507322430610657},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.30575260519981384},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1424054205417633},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.0774209201335907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8878565430641174},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.7927095890045166},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.672901451587677},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5119243860244751},{"id":"https://openalex.org/C2777283802","wikidata":"https://www.wikidata.org/wiki/Q2042963","display_name":"Picard group","level":3,"score":0.4571913778781891},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42141324281692505},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37507322430610657},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30575260519981384},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1424054205417633},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.0774209201335907},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1112/s1461157012001040","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157012001040","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2D7CD1B508808A5BA8B919F9626BDDF3/S1461157012001040a.pdf/div-class-title-zariski-chambers-on-surfaces-of-high-picard-number-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1204.4373","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.4373","pdf_url":"https://arxiv.org/pdf/1204.4373","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.749.8001","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.749.8001","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/1204.4373.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1112/s1461157012001040","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157012001040","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2D7CD1B508808A5BA8B919F9626BDDF3/S1461157012001040a.pdf/div-class-title-zariski-chambers-on-surfaces-of-high-picard-number-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2003429475.pdf","grobid_xml":"https://content.openalex.org/works/W2003429475.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W53692629","https://openalex.org/W150691015","https://openalex.org/W642007974","https://openalex.org/W1574846222","https://openalex.org/W1874023610","https://openalex.org/W1978873823","https://openalex.org/W2032951732","https://openalex.org/W2057336201","https://openalex.org/W2059884263","https://openalex.org/W2082122984","https://openalex.org/W2139787113","https://openalex.org/W2161330625","https://openalex.org/W2950042396","https://openalex.org/W2963198376","https://openalex.org/W2963628090","https://openalex.org/W4230989983","https://openalex.org/W6641875435","https://openalex.org/W6658545634","https://openalex.org/W6670847597"],"related_works":["https://openalex.org/W2000297171","https://openalex.org/W4297058887","https://openalex.org/W2777256819","https://openalex.org/W4221159894","https://openalex.org/W4299284326","https://openalex.org/W4307280152","https://openalex.org/W4288563609","https://openalex.org/W2383782903","https://openalex.org/W4251748586","https://openalex.org/W2963001884"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"an":[3,42],"improved":[4],"algorithm":[5,17],"for":[6],"the":[7,20,47,53,56],"computation":[8],"of":[9,31,38,49],"Zariski":[10],"chambers":[11,39,50],"on":[12,55],"algebraic":[13],"surfaces.":[14],"The":[15],"new":[16],"significantly":[18],"outperforms":[19],"currently":[21],"available":[22],"method":[23],"and":[24],"therefore":[25],"allows":[26],"us":[27],"to":[28],"treat":[29],"surfaces":[30],"high":[32],"Picard":[33],"number,":[34],"where":[35],"huge":[36],"numbers":[37],"occur.":[40],"As":[41],"application,":[43],"we":[44],"efficiently":[45],"compute":[46],"number":[48],"supported":[51],"by":[52],"lines":[54],"Segre\u2013Schur":[57],"quartic.":[58]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}