{"id":"https://openalex.org/W7213410474","doi":"https://doi.org/10.48550/arxiv.2609.17502","title":"Extending Andreotti's proof of Torelli's theorem to nodal curves","display_name":"Extending Andreotti's proof of Torelli's theorem to nodal curves","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213410474","doi":"https://doi.org/10.48550/arxiv.2609.17502"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17502","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17502","pdf_url":"https://arxiv.org/pdf/2609.17502","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/2609.17502","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073040305","display_name":"Alex Abreu","orcid":"https://orcid.org/0000-0002-8349-0097","observed_orcids":["https://orcid.org/0000-0002-8349-0097"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abreu, Alex","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074906510","display_name":"Marco Pacini","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pacini, Marco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5049019362","display_name":"Nicola Pagani","orcid":"https://orcid.org/0000-0002-3906-455X","observed_orcids":["https://orcid.org/0000-0002-3906-455X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pagani, Nicola","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":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":1.0,"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"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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/torelli-theorem","display_name":"Torelli theorem","score":0.8560000061988831},{"id":"https://openalex.org/keywords/nodal-curves","display_name":"nodal curves","score":0.968999981880188},{"id":"https://openalex.org/keywords/compactified-jacobians","display_name":"compactified Jacobians","score":0.847000002861023},{"id":"https://openalex.org/keywords/gauss-map","display_name":"Gauss map","score":0.7440000176429749},{"id":"https://openalex.org/keywords/projective-reconstruction","display_name":"projective reconstruction","score":0.5220000147819519},{"id":"https://openalex.org/keywords/boundary-strata","display_name":"boundary strata","score":0.6639999747276306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8586999773979187},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.5288000106811523},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5088000297546387},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4968999922275543},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.428600013256073},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.39070001244544983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3765000104904175},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.35830000042915344},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.3522000014781952},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C39290043","wikidata":"https://www.wikidata.org/wiki/Q1475760","display_name":"Projective plane","level":3,"score":0.3116999864578247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3010999858379364},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26910001039505005},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.2583000063896179},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.2567000091075897},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.17502","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17502","pdf_url":"https://arxiv.org/pdf/2609.17502","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.2609.17502","doi":"https://doi.org/10.48550/arxiv.2609.17502","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17502","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:2609.17502","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17502","pdf_url":"https://arxiv.org/pdf/2609.17502","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/W7213410474.pdf","grobid_xml":"https://content.openalex.org/works/W7213410474.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3172097180","https://openalex.org/W2950747572","https://openalex.org/W3097579009","https://openalex.org/W7095946003","https://openalex.org/W4396817200","https://openalex.org/W4407082141","https://openalex.org/W4313905110","https://openalex.org/W4294149838","https://openalex.org/W4287282604","https://openalex.org/W7133528428"],"abstract_inverted_index":{"Let":[0,19],"$C$":[1,50,94,117],"be":[2,26],"a":[3,87,109],"connected":[4,91],"nodal":[5,92],"curve":[6],"of":[7,16,34,49,52,55,63,69,72,77,81,103,116,134,145,151,168,193,196],"genus":[8],"$g$":[9],"over":[10,97],"an":[11],"algebraically":[12],"closed":[13],"field":[14],"$k$":[15],"characteristic":[17],"zero.":[18],"\\[":[20],"A(C)=\\Big(J(C),":[21],"{\\overline{P^{g-1}_C}},":[22],"\u0398(C)":[23],"\\Big)":[24],"\\]":[25],"the":[27,32,53,67,70,73,78,82,112,126,130,146,149,152,156,169,173,179,183,190],"stable":[28,104],"semi-abelic":[29,105],"pair":[30],"(in":[31],"sense":[33],"Alexeev)":[35],"associated":[36],"with":[37,60],"its":[38,56],"canonical":[39,47,57,83,114,158],"compactified":[40,131,170],"Jacobian":[41,171],"$\\overline{P^{g-1}_C}$":[42],"in":[43,129,189],"degree":[44],"$g-1$.":[45],"The":[46,142],"triple":[48],"consists":[51],"closure":[54],"image":[58],"together":[59],"two":[61],"sets":[62],"distinguished":[64],"points":[65],"encoding":[66],"information":[68],"images":[71],"nonseparating":[74],"nodes":[75],"and":[76,95,118,160,175],"branch":[79,143,161],"data":[80,162],"map.":[84],"We":[85],"prove":[86],"functorial":[88],"reconstruction:":[89],"given":[90],"curves":[93],"$C'$":[96],"$k$,":[98],"every":[99],"isomorphism":[100,122],"$A(C)\\cong":[101],"A(C')$":[102],"pairs":[106],"canonically":[107],"induces":[108],"projectivity":[110],"between":[111],"corresponding":[113],"triples":[115],"$C'$.":[119],"Passing":[120],"to":[121],"classes,":[123],"this":[124],"recovers":[125,155],"reconstruction":[127],"statement":[128],"Torelli":[132],"theorem":[133,198],"Caporaso-Viviani.":[135],"Our":[136],"proof":[137,195],"extends":[138],"Andreotti's":[139,194],"Gauss-map":[140],"strategy.":[141],"locus":[144],"projection":[147],"from":[148],"normalization":[150],"Gauss":[153],"graph":[154],"nonlinear":[157],"components":[159],"by":[163],"projective":[164],"biduality;":[165],"boundary":[166],"strata":[167],"recover":[172,178],"node-images;":[174],"incidence":[176],"arguments":[177],"linear":[180],"components.":[181],"Along":[182],"way,":[184],"we":[185],"repair":[186],"technical":[187],"gaps":[188],"classical":[191],"treatments":[192],"Torelli's":[197],"for":[199],"smooth":[200],"curves.":[201]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-17T00:00:00"}
