{"id":"https://openalex.org/W7220974116","doi":"https://doi.org/10.48550/arxiv.2610.08935","title":"The logarithmic generalised Kummer locus and its tropicalisation","display_name":"The logarithmic generalised Kummer locus and its tropicalisation","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220974116","doi":"https://doi.org/10.48550/arxiv.2610.08935"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08935","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08935","pdf_url":"https://arxiv.org/pdf/2610.08935","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.08935","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005351205","display_name":"Patrick Kennedy\u2013Hunt","orcid":"https://orcid.org/0000-0001-9726-6750","observed_orcids":["https://orcid.org/0000-0001-9726-6750"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kennedy-Hunt, Patrick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5005351205"],"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":0.9994999766349792,"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/T12351","display_name":"Geometry and complex manifolds","score":0.00019999999494757503,"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":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/tropicalization","display_name":"tropicalization","score":0.847000002861023},{"id":"https://openalex.org/keywords/polyhedral-complexes","display_name":"polyhedral complexes","score":0.8080000281333923},{"id":"https://openalex.org/keywords/semi-abelian-varieties","display_name":"semi-abelian varieties","score":0.8460000157356262}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8935999870300293},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.7305999994277954},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6575999855995178},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5242000222206116},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C54654531","wikidata":"https://www.wikidata.org/wiki/Q6073574","display_name":"Irreducible component","level":5,"score":0.4189999997615814},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.39969998598098755},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C150279058","wikidata":"https://www.wikidata.org/wiki/Q5761225","display_name":"Hilbert scheme","level":2,"score":0.3824000060558319},{"id":"https://openalex.org/C37253","wikidata":"https://www.wikidata.org/wiki/Q5156502","display_name":"Complete intersection","level":2,"score":0.3621000051498413},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C72587816","wikidata":"https://www.wikidata.org/wiki/Q7497063","display_name":"Shimura variety","level":3,"score":0.34869998693466187},{"id":"https://openalex.org/C205633959","wikidata":"https://www.wikidata.org/wiki/Q2494915","display_name":"Unipotent","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.3456000089645386},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.33730000257492065},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C143782950","wikidata":"https://www.wikidata.org/wiki/Q40460","display_name":"Orbifold","level":2,"score":0.3280999958515167},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.32249999046325684},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.32030001282691956},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C203492994","wikidata":"https://www.wikidata.org/wiki/Q909669","display_name":"Divisor (algebraic geometry)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2849000096321106},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2531999945640564},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.2526000142097473},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08935","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08935","pdf_url":"https://arxiv.org/pdf/2610.08935","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.2610.08935","doi":"https://doi.org/10.48550/arxiv.2610.08935","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08935","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:2610.08935","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08935","pdf_url":"https://arxiv.org/pdf/2610.08935","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220974116.pdf","grobid_xml":"https://content.openalex.org/works/W7220974116.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7154786750","https://openalex.org/W2949378395","https://openalex.org/W7117313417","https://openalex.org/W2809358887","https://openalex.org/W2019599359","https://openalex.org/W2131282624","https://openalex.org/W4386273150","https://openalex.org/W2518027754","https://openalex.org/W3189393478","https://openalex.org/W3101288187"],"abstract_inverted_index":{"We":[0,147],"construct":[1],"a":[2,7,31,42,55,87,97,101,123,199],"separated":[3],"logarithmic":[4,35,81,91,131,144,202],"compactification":[5,29,51],"of":[6,12,19,34,45,59,71,75,83,89,103,143,150,160,201,205],"divisor":[8],"in":[9,23,112,157],"the":[10,113,136,158,170,177,183,194],"moduli":[11],"polarised":[13],"irreducible":[14,188],"holomorphic":[15],"symplectic":[16],"(IHS)":[17],"varieties":[18,74],"generalised":[20,47,72,125,138,173,195],"Kummer":[21,48,73,126,139,174,196],"type":[22,114],"dimension":[24,77],"at":[25],"least":[26],"four.":[27],"This":[28,117],"carries":[30,41],"universal":[32,43],"family":[33,44,102,119],"IHS":[36],"varieties,":[37],"and":[38,62,68,78,109,153],"its":[39],"tropicalisation":[40,98],"tropical":[46,118,124,172],"varieties.":[49,146,207],"The":[50],"is":[52,120,190],"built":[53],"from":[54],"more":[56],"general":[57],"construction":[58,140,197],"explicit,":[60],"projective,":[61],"logarithmically":[63],"smooth":[64],"models":[65,164],"for":[66],"type~II":[67],"type~III":[69],"degenerations":[70,94],"arbitrary":[76],"over":[79],"base":[80,88],"schemes":[82,133],"any":[84,90],"dimension.":[85],"Over":[86],"rank,":[92],"these":[93],"come":[95],"with":[96,107,110,176],"map":[99],"to":[100,134,141,166,198],"integral":[104],"affine":[105],"manifolds":[106],"singularities,":[108],"boundary":[111,159],"II":[115],"case.":[116],"constructed":[121,191],"through":[122],"construction.":[127],"Our":[128],"approach":[129],"uses":[130],"Hilbert":[132],"extend":[135],"conventional":[137],"families":[142],"abelian":[145],"describe":[148],"fibres":[149],"our":[151,161],"degenerations,":[152],"thus":[154],"every":[155],"point":[156],"compactification.":[162],"Proper":[163],"correspond":[165],"polyhedral":[167,179],"structures":[168],"on":[169],"associated":[171],"variety,":[175],"resulting":[178],"complex":[180],"serving":[181],"as":[182],"dual":[184],"intersection":[185],"complex;":[186],"each":[187],"component":[189],"by":[192],"applying":[193],"product":[200],"group":[203],"compactifications":[204],"semi-abelian":[206]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-09T00:00:00"}