{"id":"https://openalex.org/W4388028126","doi":"https://doi.org/10.14231/ag-2023-024","title":"Factorization centers in dimension 2 and the Grothendieck ring of varieties","display_name":"Factorization centers in dimension 2 and the Grothendieck ring of varieties","publication_year":2023,"publication_date":"2023-10-30","ids":{"openalex":"https://openalex.org/W4388028126","doi":"https://doi.org/10.14231/ag-2023-024"},"language":"en","primary_location":{"id":"doi:10.14231/ag-2023-024","doi":"https://doi.org/10.14231/ag-2023-024","is_oa":true,"landing_page_url":"https://doi.org/10.14231/ag-2023-024","pdf_url":"https://doi.org/10.14231/ag-2023-024","source":{"id":"https://openalex.org/S4210177002","display_name":"Algebraic geometry","issn_l":"2313-1691","issn":["2313-1691","2214-2584"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","norway-2","oarl","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318578","host_organization_name":"Foundation Compositio Mathematica","host_organization_lineage":["https://openalex.org/P4310318578"],"host_organization_lineage_names":["Foundation Compositio Mathematica"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algebraic Geometry","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.14231/ag-2023-024","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074998203","display_name":"Hsueh-Yung Lin","orcid":"https://orcid.org/0000-0001-8672-7742","observed_orcids":["https://orcid.org/0000-0001-8672-7742"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hsueh-Yung Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041949924","display_name":"Evgeny Shinder","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Evgeny Shinder","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5013165823","display_name":"Susanna Zimmermann","orcid":"https://orcid.org/0000-0002-2216-7712","observed_orcids":["https://orcid.org/0000-0002-2216-7712"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Susanna Zimmermann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0638,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.84749065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"666","last_page":"693"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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/T11680","display_name":"Advanced Algebra and Geometry","score":9.999999747378752e-05,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/weak-factorization","display_name":"weak factorization","score":0.7789999842643738},{"id":"https://openalex.org/keywords/birational-maps","display_name":"birational maps","score":0.8149999976158142},{"id":"https://openalex.org/keywords/birational-automorphisms","display_name":"birational automorphisms","score":0.847000002861023},{"id":"https://openalex.org/keywords/smooth-projective-surfaces","display_name":"smooth projective surfaces","score":0.8259999752044678},{"id":"https://openalex.org/keywords/perfect-fields","display_name":"perfect fields","score":0.9350000023841858},{"id":"https://openalex.org/keywords/grothendieck-ring-of-varieties","display_name":"Grothendieck ring of varieties","score":0.9829999804496765},{"id":"https://openalex.org/keywords/l-equivalence","display_name":"L-equivalence","score":0.8840000033378601},{"id":"https://openalex.org/keywords/rational-surfaces","display_name":"rational surfaces","score":0.9240000247955322}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.668448805809021},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.6675281524658203},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5876635313034058},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5633622407913208},{"id":"https://openalex.org/C122022638","wikidata":"https://www.wikidata.org/wiki/Q1128678","display_name":"Grothendieck group","level":3,"score":0.4268037676811218},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3766605257987976},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3454025685787201},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3354932963848114},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09487181901931763},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05645465850830078},{"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/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.14231/ag-2023-024","doi":"https://doi.org/10.14231/ag-2023-024","is_oa":true,"landing_page_url":"https://doi.org/10.14231/ag-2023-024","pdf_url":"https://doi.org/10.14231/ag-2023-024","source":{"id":"https://openalex.org/S4210177002","display_name":"Algebraic geometry","issn_l":"2313-1691","issn":["2313-1691","2214-2584"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","norway-2","oarl","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318578","host_organization_name":"Foundation Compositio Mathematica","host_organization_lineage":["https://openalex.org/P4310318578"],"host_organization_lineage_names":["Foundation Compositio Mathematica"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algebraic Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.14231/ag-2023-024","doi":"https://doi.org/10.14231/ag-2023-024","is_oa":true,"landing_page_url":"https://doi.org/10.14231/ag-2023-024","pdf_url":"https://doi.org/10.14231/ag-2023-024","source":{"id":"https://openalex.org/S4210177002","display_name":"Algebraic geometry","issn_l":"2313-1691","issn":["2313-1691","2214-2584"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-b","jufo-1","norway-2","oarl","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310318578","host_organization_name":"Foundation Compositio Mathematica","host_organization_lineage":["https://openalex.org/P4310318578"],"host_organization_lineage_names":["Foundation Compositio Mathematica"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algebraic Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2134641055","display_name":"DERIVED CATEGORIES AND ALGEBRAIC K-THEORY OF SINGULARITIES","funder_award_id":"EP/T019379/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3705856723","display_name":"Fibrations and algebraic group actions","funder_award_id":"ANR-18-CE40-0003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4656594441","display_name":null,"funder_award_id":"ANR18","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320311041","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320320912","display_name":"Ministry of Education, Culture, Sports, Science and Technology","ror":"https://ror.org/048rj2z13"},{"id":"https://openalex.org/F4320327974","display_name":"Conseil R\u00e9gional des Pays de la Loire","ror":"https://ror.org/01zsm1k25"},{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388028126.pdf","grobid_xml":"https://content.openalex.org/works/W4388028126.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W367145261","https://openalex.org/W1484379759","https://openalex.org/W1494026294","https://openalex.org/W1520833136","https://openalex.org/W1538392730","https://openalex.org/W1591940114","https://openalex.org/W1596185498","https://openalex.org/W1597808462","https://openalex.org/W1650316289","https://openalex.org/W1761437831","https://openalex.org/W1968436870","https://openalex.org/W1986399936","https://openalex.org/W1989214109","https://openalex.org/W2030521142","https://openalex.org/W2094403984","https://openalex.org/W2134094702","https://openalex.org/W2142457098","https://openalex.org/W2150418852","https://openalex.org/W2178202678","https://openalex.org/W2204040005","https://openalex.org/W2248896763","https://openalex.org/W2307393813","https://openalex.org/W2583205343","https://openalex.org/W2741151869","https://openalex.org/W2891854343","https://openalex.org/W2893834108","https://openalex.org/W2954545836","https://openalex.org/W2964229745","https://openalex.org/W3080732118","https://openalex.org/W3124848678","https://openalex.org/W3203871380","https://openalex.org/W4240787581","https://openalex.org/W4245388614","https://openalex.org/W4252841308","https://openalex.org/W4283749584","https://openalex.org/W4310562088","https://openalex.org/W4390431997","https://openalex.org/W4406717288","https://openalex.org/W4416147203"],"related_works":["https://openalex.org/W3112289063","https://openalex.org/W2123499714","https://openalex.org/W7123671627","https://openalex.org/W4394643246","https://openalex.org/W7099519067","https://openalex.org/W2020842652","https://openalex.org/W7097769874","https://openalex.org/W1604912599","https://openalex.org/W7096190424","https://openalex.org/W1589137156"],"abstract_inverted_index":{"We":[0],"initiate":[1],"the":[2,43,49],"study":[3],"of":[4,7,32,56,62,72,105],"factorization":[5,55],"centers":[6,45,51,79],"birational":[8,26,70],"maps":[9],"and":[10],"complete":[11],"it":[12],"for":[13,24,83],"surfaces":[14],"over":[15,38],"a":[16,33,39,73,91],"perfect":[17,40],"field":[18,41],"in":[19,52,101],"this":[20],"article.We":[21],"prove":[22],"that":[23,59,77],"every":[25,53,84],"automorphism":[27],"\u03d5":[28],":":[29],"X":[30,31,37],"smooth":[34],"projective":[35],"surface":[36,86],"k,":[42],"blowup":[44],"are":[46,80],"isomorphic":[47],"to":[48,95],"blowdown":[50],"weak":[54],"\u03d5.This":[57],"implies":[58,76],"nontrivial":[60],"L-equivalences":[61],"zero-dimensional":[63,92],"varieties":[64],"cannot":[65],"be":[66],"constructed":[67],"based":[68],"on":[69],"automorphisms":[71],"surface.It":[74],"also":[75],"rationality":[78,103],"well":[81],"defined":[82],"rational":[85],"X;":[87],"namely,":[88],"there":[89],"exists":[90],"variety":[93],"intrinsic":[94],"X,":[96],"which":[97],"is":[98],"blown":[99],"up":[100],"any":[102],"construction":[104],"X.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2023-11-01T00:00:00"}