{"id":"https://openalex.org/W7214724636","doi":"https://doi.org/10.48550/arxiv.2609.35683","title":"On orbits of the automorphism group of toroidal spherical varieties","display_name":"On orbits of the automorphism group of toroidal spherical varieties","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214724636","doi":"https://doi.org/10.48550/arxiv.2609.35683"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35683","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35683","pdf_url":"https://arxiv.org/pdf/2609.35683","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.35683","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152135442","display_name":"Alexander Chernov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chernov, Alexander","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5153477389","display_name":"Klim Rolgin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rolgin, Klim","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":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.5425000190734863,"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":0.5425000190734863,"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":0.44290000200271606,"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/T12351","display_name":"Geometry and complex manifolds","score":0.004900000058114529,"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/divisor-class-group","display_name":"divisor class group","score":0.75},{"id":"https://openalex.org/keywords/monoids","display_name":"monoids","score":0.531000018119812},{"id":"https://openalex.org/keywords/algebraic-groups","display_name":"algebraic groups","score":0.49000000953674316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8420000076293945},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.7168999910354614},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6814000010490417},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.5649999976158142},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5450999736785889},{"id":"https://openalex.org/C15001198","wikidata":"https://www.wikidata.org/wiki/Q3241394","display_name":"Toroid","level":3,"score":0.5351999998092651},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.49799999594688416},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.489300012588501},{"id":"https://openalex.org/C124453015","wikidata":"https://www.wikidata.org/wiki/Q1139583","display_name":"Inner automorphism","level":4,"score":0.4763999879360199},{"id":"https://openalex.org/C7619685","wikidata":"https://www.wikidata.org/wiki/Q3630548","display_name":"Outer automorphism group","level":4,"score":0.47450000047683716},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4722999930381775},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.46380001306533813},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.44749999046325684},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.44589999318122864},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.44110000133514404},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4090000092983246},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4088999927043915},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.3474000096321106},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.3237000107765198},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.31610000133514404},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.2872999906539917},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.25929999351501465},{"id":"https://openalex.org/C185579658","wikidata":"https://www.wikidata.org/wiki/Q3554813","display_name":"Affine variety","level":3,"score":0.257999986410141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.257099986076355}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35683","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35683","pdf_url":"https://arxiv.org/pdf/2609.35683","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.35683","doi":"https://doi.org/10.48550/arxiv.2609.35683","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35683","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.35683","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35683","pdf_url":"https://arxiv.org/pdf/2609.35683","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214724636.pdf","grobid_xml":"https://content.openalex.org/works/W7214724636.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4312891450","https://openalex.org/W4389471160","https://openalex.org/W4417292644","https://openalex.org/W7111241516"],"related_works":["https://openalex.org/W4280520695","https://openalex.org/W4312891450","https://openalex.org/W4402396911","https://openalex.org/W4399333054","https://openalex.org/W4313192770","https://openalex.org/W2027214993","https://openalex.org/W2985988392","https://openalex.org/W7128472618","https://openalex.org/W2951568088","https://openalex.org/W4310556872"],"abstract_inverted_index":{"In":[0,16],"this":[1],"paper":[2],"we":[3,20,72],"study":[4],"the":[5,8,17,27,31,38,41,44,78,82],"orbits":[6],"of":[7,30,40,61,84],"automorphism":[9],"group":[10,47],"on":[11],"a":[12,66,74,92],"toroidal":[13,69],"spherical":[14,70],"variety.":[15],"affine":[18],"case,":[19],"prove":[21],"that":[22,88],"two":[23],"points":[24],"lie":[25],"in":[26,59],"same":[28],"orbit":[29],"identity":[32],"component":[33],"if":[34,37],"and":[35],"only":[36],"kernels":[39,56],"homomorphisms":[42],"from":[43],"divisor":[45,51],"class":[46,52],"to":[48],"their":[49],"local":[50],"groups":[53],"coincide.":[54],"These":[55],"are":[57],"described":[58],"terms":[60],"$B$-stable":[62,85],"prime":[63,86],"divisors.":[64],"For":[65],"smooth":[67],"complete":[68],"variety,":[71],"obtain":[73],"similar":[75],"criterion":[76],"using":[77],"monoids":[79],"generated":[80],"by":[81],"classes":[83],"divisors":[87],"do":[89],"not":[90],"contain":[91],"given":[93],"$G$-orbit.":[94]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
