{"id":"https://openalex.org/W7214094483","doi":"https://doi.org/10.48550/arxiv.2609.26521","title":"Irrational Seshadri constants from dihedral orbits","display_name":"Irrational Seshadri constants from dihedral orbits","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214094483","doi":"https://doi.org/10.48550/arxiv.2609.26521"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26521","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26521","pdf_url":"https://arxiv.org/pdf/2609.26521","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/2609.26521","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055936436","display_name":"Antonio Laface","orcid":"https://orcid.org/0000-0001-6926-8249","observed_orcids":["https://orcid.org/0000-0001-6926-8249"]},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["CL","IT"],"is_corresponding":false,"raw_author_name":"Laface, Antonio","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidad de Concepci\u00f3n , Casilla 160-C , Concepci\u00f3n , Chile","Dipartimento di Matematica e Informatica , Universit\u00e0 degli studi di Palermo , Via Archirafi 34 , 90123 Palermo , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidad de Concepci\u00f3n , Casilla 160-C , Concepci\u00f3n , Chile","institution_ids":["https://openalex.org/I172787465"]},{"raw_affiliation_string":"Dipartimento di Matematica e Informatica , Universit\u00e0 degli studi di Palermo , Via Archirafi 34 , 90123 Palermo , Italy","institution_ids":["https://openalex.org/I900890020"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090912842","display_name":"Luca Ugaglia","orcid":"https://orcid.org/0000-0002-4149-6407","observed_orcids":["https://orcid.org/0000-0002-4149-6407"]},"institutions":[{"id":"https://openalex.org/I172787465","display_name":"University of Concepci\u00f3n","ror":"https://ror.org/0460jpj73","country_code":"CL","type":"education","lineage":["https://openalex.org/I172787465"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Ugaglia, Luca","raw_affiliation_strings":["Departamento de Matem\u00e1tica , Universidad de Concepci\u00f3n , Casilla 160-C , Concepci\u00f3n , Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica , Universidad de Concepci\u00f3n , Casilla 160-C , Concepci\u00f3n , Chile","institution_ids":["https://openalex.org/I172787465"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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":0.9976000189781189,"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":0.9976000189781189,"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":0.001500000013038516,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/seshadri-constants","display_name":"Seshadri constants","score":0.9660000205039978},{"id":"https://openalex.org/keywords/dihedral-groups","display_name":"dihedral groups","score":0.7089999914169312},{"id":"https://openalex.org/keywords/minimal-resolution","display_name":"minimal resolution","score":0.7839999794960022},{"id":"https://openalex.org/keywords/plane-model","display_name":"plane model","score":0.6110000014305115}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8011000156402588},{"id":"https://openalex.org/C94931360","wikidata":"https://www.wikidata.org/wiki/Q607728","display_name":"Irrational number","level":2,"score":0.7107999920845032},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7001000046730042},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5936999917030334},{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.5419999957084656},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.453000009059906},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40369999408721924},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.39559999108314514},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38359999656677246},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.37529999017715454},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.3711000084877014},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.3707999885082245},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3386000096797943},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3240000009536743},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C2781458696","wikidata":"https://www.wikidata.org/wiki/Q7307244","display_name":"Reflection group","level":4,"score":0.2759999930858612}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26521","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26521","pdf_url":"https://arxiv.org/pdf/2609.26521","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.2609.26521","doi":"https://doi.org/10.48550/arxiv.2609.26521","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26521","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:2609.26521","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26521","pdf_url":"https://arxiv.org/pdf/2609.26521","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":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":"https://ror.org/00b9dvn87"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214094483.pdf","grobid_xml":"https://content.openalex.org/works/W7214094483.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1580842374","https://openalex.org/W2020055761","https://openalex.org/W2516571265","https://openalex.org/W2622018787","https://openalex.org/W4399795360"],"related_works":["https://openalex.org/W7215744641","https://openalex.org/W2622018787","https://openalex.org/W3005965176","https://openalex.org/W2516571265","https://openalex.org/W2909685305","https://openalex.org/W2140573969","https://openalex.org/W1480639614","https://openalex.org/W4394973266","https://openalex.org/W1513508487","https://openalex.org/W4414230711"],"abstract_inverted_index":{"We":[0,64],"construct":[1],"an":[2,88],"irrational":[3,89],"one-point":[4,90],"Seshadri":[5,40,91],"constant":[6,41,92],"on":[7,93,116],"the":[8,39,52,61,68,94,109,114],"blow-up":[9,110],"$X_9$":[10],"of":[11,42,78,83,101,108],"$\\mathbb{P}^2$":[12],"at":[13,26,44,72],"nine":[14],"very":[15,28,46,74],"general":[16,29,47,75],"points.":[17],"The":[18],"divisor":[19],"$L=9H-3(E_1+\\cdots+E_5)-2(E_6+\\cdots+E_9)$":[20],"is":[21,49],"ample":[22],"and":[23,58,105],"satisfies":[24],"$\\varepsilon(L;x)=2\\sqrt{5}$":[25],"a":[27,73,79,106],"point":[30],"$x\\in":[31],"X_9$.":[32],"To":[33],"prove":[34,66],"this,":[35],"we":[36],"establish":[37],"that":[38,67],"$\\mathcal{O}_{\\mathbb{P}^1\\times\\mathbb{P}^1}(1,1)$":[43],"ten":[45],"points":[48],"$1/\\sqrt{5}$,":[50],"completing":[51],"reflection":[53],"approach":[54],"proposed":[55],"by":[56],"Dionne":[57],"Roth":[59],"for":[60],"ten-point":[62],"case.":[63],"also":[65],"same":[69],"equality":[70],"holds":[71],"free":[76],"orbit":[77],"fixed":[80],"dihedral":[81],"group":[82],"order":[84],"ten.":[85],"This":[86],"yields":[87],"singular":[95],"quotient":[96],"surface.":[97],"A":[98],"plane":[99],"model":[100],"its":[102],"minimal":[103],"resolution":[104],"deformation":[107],"centers":[111],"then":[112],"give":[113],"result":[115],"$X_9$.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}