{"id":"https://openalex.org/W7220965487","doi":"https://doi.org/10.48550/arxiv.2610.08608","title":"Derived supergeometry and perfect obstruction theories on algebraic superstacks","display_name":"Derived supergeometry and perfect obstruction theories on algebraic superstacks","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220965487","doi":"https://doi.org/10.48550/arxiv.2610.08608"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.08608","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08608","pdf_url":"https://arxiv.org/pdf/2610.08608","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/2610.08608","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044421016","display_name":"Ugo Bruzzo","orcid":"https://orcid.org/0000-0001-8726-1729","observed_orcids":["https://orcid.org/0000-0001-8726-1729"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruzzo, Ugo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010144528","display_name":"Daniel Hern\u00e1ndez Ruip\u00e9rez","orcid":"https://orcid.org/0000-0002-8787-4354","observed_orcids":["https://orcid.org/0000-0002-8787-4354"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ruip\u00e9rez, Daniel Hern\u00e1ndez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021756043","display_name":"Emanuele Pavia","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pavia, Emanuele","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023551453","display_name":"Andrea T. Ricolfi","orcid":"https://orcid.org/0000-0002-8172-2026","observed_orcids":["https://orcid.org/0000-0002-8172-2026"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ricolfi, Andrea T.","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":0.9541000127792358,"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":0.9541000127792358,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.03920000046491623,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.004000000189989805,"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/perfect-obstruction-theory","display_name":"perfect obstruction theory","score":0.9229999780654907},{"id":"https://openalex.org/keywords/deformation-theory","display_name":"deformation theory","score":0.6549999713897705},{"id":"https://openalex.org/keywords/moduli-space-of-stable-maps","display_name":"moduli space of stable maps","score":0.7310000061988831},{"id":"https://openalex.org/keywords/virtual-dimension","display_name":"virtual dimension","score":0.8140000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8202999830245972},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6022999882698059},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5450999736785889},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.510699987411499},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.42910000681877136},{"id":"https://openalex.org/C54654531","wikidata":"https://www.wikidata.org/wiki/Q6073574","display_name":"Irreducible component","level":5,"score":0.39809998869895935},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.36739999055862427},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C168185519","wikidata":"https://www.wikidata.org/wiki/Q5156577","display_name":"Complex dimension","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.3264000117778778},{"id":"https://openalex.org/C2731732","wikidata":"https://www.wikidata.org/wiki/Q7301119","display_name":"Real algebraic geometry","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.3089999854564667},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.3082999885082245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3050000071525574},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C26959085","wikidata":"https://www.wikidata.org/wiki/Q5275330","display_name":"Differential algebraic geometry","level":5,"score":0.2935999929904938},{"id":"https://openalex.org/C10996884","wikidata":"https://www.wikidata.org/wiki/Q5508773","display_name":"Function field of an algebraic variety","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C69653121","wikidata":"https://www.wikidata.org/wiki/Q1434805","display_name":"Algebraic surface","level":3,"score":0.28459998965263367},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.2815000116825104},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2782000005245209},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.27790001034736633},{"id":"https://openalex.org/C185382297","wikidata":"https://www.wikidata.org/wiki/Q16959942","display_name":"Derived algebraic geometry","level":5,"score":0.27160000801086426},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C18109118","wikidata":"https://www.wikidata.org/wiki/Q5251702","display_name":"Deformation theory","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.2526000142097473},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.08608","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08608","pdf_url":"https://arxiv.org/pdf/2610.08608","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.2610.08608","doi":"https://doi.org/10.48550/arxiv.2610.08608","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.08608","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.08608","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.08608","pdf_url":"https://arxiv.org/pdf/2610.08608","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":[{"id":"https://openalex.org/G281753772","display_name":null,"funder_award_id":"MTM2017-86042-P","funder_id":"https://openalex.org/F4320326262","funder_display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320326262","display_name":"Ministerio de Asuntos Econ\u00f3micos y Transformaci\u00f3n Digital, Gobierno de Espa\u00f1a","ror":"https://ror.org/03sv46s19"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220965487.pdf","grobid_xml":"https://content.openalex.org/works/W7220965487.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1480752835","https://openalex.org/W1728442826","https://openalex.org/W4414876084","https://openalex.org/W4415065789","https://openalex.org/W4416048034","https://openalex.org/W4416557679","https://openalex.org/W6910804653"],"related_works":["https://openalex.org/W1969744210","https://openalex.org/W4416557679","https://openalex.org/W2165926301","https://openalex.org/W4416048034","https://openalex.org/W6888954754","https://openalex.org/W7164161576","https://openalex.org/W1597178391","https://openalex.org/W2660454564","https://openalex.org/W7214086170","https://openalex.org/W4298840120"],"abstract_inverted_index":{"We":[0,68,94,127],"develop":[1],"a":[2,71,81,87,122,129,166],"deformation-theoretic":[3,167],"framework":[4],"for":[5,65,176],"algebraic":[6,37,66,77],"superstacks":[7],"and":[8,33,60,113,117,135,179],"apply":[9],"it":[10],"to":[11,26,41,97,181],"the":[12,31,42,51,98,101,143,170,182,187],"construction":[13],"of":[14,21,53,75,100,105,108,115,169,186,191],"perfect":[15,62,82],"obstruction":[16,63,83,145],"theories":[17,64],"on":[18,147],"moduli":[19,189],"spaces":[20],"stable":[22,106,177,192],"supermaps.":[23],"In":[24],"order":[25],"achieve":[27],"this":[28,85],"we":[29,140,152],"employ":[30],"tools":[32],"concepts":[34],"from":[35,90],"derived":[36,54,73,131],"geometry,":[38],"extending":[39],"them":[40],"supergeometric":[43],"setting.":[44],"Our":[45],"main":[46],"technical":[47],"contributions":[48],"are":[49],"(i)":[50],"notions":[52],"superstacks,":[55],"(ii)":[56],"their":[57],"cotangent":[58,138],"supercomplexes":[59],"(iii)":[61],"superstacks.":[67],"prove":[69,141],"that":[70,142],"quasi-smooth":[72],"enhancement":[74,132],"an":[76],"superstack":[78,103],"always":[79],"yields":[80],"theory:":[84],"generalizes":[86],"well-known":[88],"principle":[89],"classical":[91,188],"deformation":[92],"theory.":[93],"then":[95],"turn":[96],"case":[99],"Deligne--Mumford":[102],"$\\boldsymbol{\\mathcal{M}}^{\\mathsf{st-}\\mathrm{SUSY}}_{g,\\mathfrak{n}}(\\boldsymbol{Y})$":[104,148],"supermaps":[107,178],"fixed":[109],"genus,":[110],"homology":[111],"class":[112],"numbers":[114],"Neveu--Schwarz":[116],"Ramond--Ramond":[118],"punctures,":[119],"with":[120],"target":[121],"smooth":[123],"projective":[124],"superscheme":[125],"$\\boldsymbol{Y}$.":[126],"exhibit":[128],"natural":[130],"$\\mathbb{R}":[133],"\\boldsymbol{\\mathcal{M}}^{\\mathsf{st-}\\mathrm{SUSY}}_{g,\\mathfrak{n}}(\\boldsymbol{Y})$":[134],"compute":[136,153],"its":[137,154],"supercomplex;":[139],"induced":[144],"theory":[146],"is":[149],"perfect.":[150],"Finally,":[151],"virtual":[155,171,184],"dimension":[156,172,185],"by":[157],"super":[158],"Grothendieck--Riemann--Roch.":[159],"The":[160],"resulting":[161],"formula":[162,173],"gives,":[163],"in":[164],"particular,":[165],"proof":[168],"previously":[174],"conjectured":[175],"specializes":[180],"usual":[183],"stack":[190],"maps.":[193]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
