{"id":"https://openalex.org/W7222985115","doi":"https://doi.org/10.48550/arxiv.2610.23224","title":"Regularity, depth and Serre depth of symbolic powers of complementary edge ideals","display_name":"Regularity, depth and Serre depth of symbolic powers of complementary edge ideals","publication_year":2026,"publication_date":"2026-10-16","ids":{"openalex":"https://openalex.org/W7222985115","doi":"https://doi.org/10.48550/arxiv.2610.23224"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.23224","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23224","pdf_url":"https://arxiv.org/pdf/2610.23224","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/2610.23224","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064405400","display_name":"Antonino Ficarra","orcid":"https://orcid.org/0000-0001-6205-9524","observed_orcids":["https://orcid.org/0000-0001-6205-9524"]},"institutions":[{"id":"https://openalex.org/I4210116604","display_name":"Ilam University","ror":"https://ror.org/01r277z15","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210116604"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ficarra, Antonino","raw_affiliation_strings":["Department of Mathematics , Faculty of Science , Ilam University , P.O.Box 69315-516 , Ilam , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Science , Ilam University , P.O.Box 69315-516 , Ilam , Iran","institution_ids":["https://openalex.org/I4210116604"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025550368","display_name":"Somayeh Moradi","orcid":"https://orcid.org/0000-0002-7704-2626","observed_orcids":["https://orcid.org/0000-0002-7704-2626"]},"institutions":[{"id":"https://openalex.org/I163770644","display_name":"Okayama University","ror":"https://ror.org/02pc6pc55","country_code":"JP","type":"education","lineage":["https://openalex.org/I163770644"]},{"id":"https://openalex.org/I4210116604","display_name":"Ilam University","ror":"https://ror.org/01r277z15","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210116604"]}],"countries":["IR","JP"],"is_corresponding":false,"raw_author_name":"Moradi, Somayeh","raw_affiliation_strings":["Department of Mathematics , Faculty of Science , Ilam University , P.O.Box 69315-516 , Ilam , Iran","Department of Mathematics , Okayama University , 3-1-1 Tsushima-naka , Kita-ku , Okayama 700-8530 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Science , Ilam University , P.O.Box 69315-516 , Ilam , Iran","institution_ids":["https://openalex.org/I4210116604"]},{"raw_affiliation_string":"Department of Mathematics , Okayama University , 3-1-1 Tsushima-naka , Kita-ku , Okayama 700-8530 Japan","institution_ids":["https://openalex.org/I163770644"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5149243863","display_name":"Yuji Muta","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210116604","display_name":"Ilam University","ror":"https://ror.org/01r277z15","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210116604"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Muta, Yuji","raw_affiliation_strings":["Department of Mathematics , Faculty of Science , Ilam University , P.O.Box 69315-516 , Ilam , Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Faculty of Science , Ilam University , P.O.Box 69315-516 , Ilam , Iran","institution_ids":["https://openalex.org/I4210116604"]}]}],"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":2,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9994999766349792,"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/T11703","display_name":"Rings, Modules, and Algebras","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/T11435","display_name":"Polynomial and algebraic computation","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symbolic-power","display_name":"symbolic power","score":0.968999981880188},{"id":"https://openalex.org/keywords/castelnuovo-mumford-regularity","display_name":"Castelnuovo-Mumford regularity","score":0.9919999837875366},{"id":"https://openalex.org/keywords/depth","display_name":"depth","score":0.6639999747276306},{"id":"https://openalex.org/keywords/cohen-macaulayness","display_name":"Cohen-Macaulayness","score":0.8420000076293945},{"id":"https://openalex.org/keywords/linear-resolution","display_name":"linear resolution","score":0.8330000042915344},{"id":"https://openalex.org/keywords/squarefree-monomial-ideals","display_name":"squarefree monomial ideals","score":0.8529999852180481},{"id":"https://openalex.org/keywords/local-cohomology-modules","display_name":"local cohomology modules","score":0.8880000114440918},{"id":"https://openalex.org/keywords/finite-simple-graphs","display_name":"finite simple graphs","score":0.7749999761581421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9004999995231628},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.7056999802589417},{"id":"https://openalex.org/C2777789435","wikidata":"https://www.wikidata.org/wiki/Q19369206","display_name":"Monomial ideal","level":4,"score":0.6085000038146973},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.5460000038146973},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4799000024795532},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45969998836517334},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.45419999957084656},{"id":"https://openalex.org/C2776095079","wikidata":"https://www.wikidata.org/wiki/Q489538","display_name":"The Symbolic","level":2,"score":0.4453999996185303},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.4101000130176544},{"id":"https://openalex.org/C2779626591","wikidata":"https://www.wikidata.org/wiki/Q536936","display_name":"Symbolic power","level":3,"score":0.40709999203681946},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35899999737739563},{"id":"https://openalex.org/C23123167","wikidata":"https://www.wikidata.org/wiki/Q7661193","display_name":"Symbolic trajectory evaluation","level":3,"score":0.32850000262260437},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C2777041388","wikidata":"https://www.wikidata.org/wiki/Q6664297","display_name":"Local cohomology","level":3,"score":0.2906999886035919},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.2705000042915344}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.23224","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23224","pdf_url":"https://arxiv.org/pdf/2610.23224","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.2610.23224","doi":"https://doi.org/10.48550/arxiv.2610.23224","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.23224","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:2610.23224","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.23224","pdf_url":"https://arxiv.org/pdf/2610.23224","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/G3566981129","display_name":null,"funder_award_id":"JDC2023-051705-I","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222985115.pdf","grobid_xml":"https://content.openalex.org/works/W7222985115.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W4414746983","https://openalex.org/W4415886204","https://openalex.org/W4416361851","https://openalex.org/W6910644182","https://openalex.org/W6967522749","https://openalex.org/W7130745801","https://openalex.org/W7133506298","https://openalex.org/W7134268312","https://openalex.org/W7138380871","https://openalex.org/W7138912129","https://openalex.org/W7206193609","https://openalex.org/W7211990224","https://openalex.org/W7212076284"],"related_works":["https://openalex.org/W7211990224","https://openalex.org/W7212076284","https://openalex.org/W7206193609","https://openalex.org/W4414746983","https://openalex.org/W4220836288","https://openalex.org/W2970874440","https://openalex.org/W3199703323","https://openalex.org/W3000004661","https://openalex.org/W4399569064","https://openalex.org/W2727439189"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2,162],"a":[3],"finite":[4],"simple":[5],"graph":[6],"and":[7,25,43,54,70,99,127,134,174,199],"let":[8],"$I_c(G)$":[9],"denote":[10],"its":[11,95],"complementary":[12,77,141,167,186],"edge":[13,78,142,168,187],"ideal.":[14],"In":[15,189],"this":[16,139],"paper,":[17],"we":[18,65,115,144,165,191],"study":[19],"the":[20,23,31,52,55,58,73,86,103,117,132,135,153,156,176,201],"Castelnuovo-Mumford":[21],"regularity,":[22],"depth":[24,27,88,133,158,178],"Serre":[26,136,177],"for":[28,40,46,97,102,108,123,131,149,179,205],"$(S_{2})$":[29,180,198],"of":[30,34,51,57,61,76,121,181,185,195,200,203],"symbolic":[32,74,87,125,157,183],"powers":[33,75,184],"$I_c(G)$.":[35],"We":[36,83,92],"derive":[37,128],"explicit":[38],"formulas":[39],"$\\operatorname{reg}":[41,44],"I_c(G)^{(k)}$":[42],"I_c(G)^{(k)}/I_c(G)^k$":[45],"every":[47,206],"$k\\geq1$,":[48],"in":[49],"terms":[50],"number":[53],"sizes":[56],"connected":[59],"components":[60],"$G$.":[62],"As":[63],"applications,":[64],"determine":[66,93,175],"their":[67],"asymptotic":[68,104],"behavior,":[69],"completely":[71],"characterize":[72,166],"ideals":[79,169],"having":[80],"linear":[81],"resolutions.":[82],"then":[84],"investigate":[85],"function":[89,159],"$k\\mapsto\\operatorname{depth}":[90],"S/I_c(G)^{(k)}$.":[91],"explicitly":[94],"values":[96],"$k=2,3,4$,":[98],"establish":[100],"bounds":[101],"depth.":[105,137],"More":[106],"generally,":[107],"an":[109],"arbitrary":[110],"squarefree":[111],"monomial":[112],"ideal":[113],"$I$,":[114],"compare":[116],"local":[118],"cohomology":[119],"modules":[120],"$S/I^{(k)}$":[122],"different":[124],"powers,":[126],"corresponding":[129],"inequalities":[130],"Applying":[138],"to":[140],"ideals,":[143],"obtain":[145,192],"$\\operatorname{depth}":[146],"S/I_{c}(G)^{(t)}\\geq\\operatorname{depth}":[147],"S/I_{c}(G)^{(k)}$":[148],"$k\\geq":[150,207],"2t-1$,":[151],"despite":[152],"fact":[154],"that":[155],"need":[160],"not":[161],"non-increasing.":[163],"Finally,":[164],"satisfying":[170],"Serre's":[171,196],"condition":[172,197],"$(S_r)$,":[173],"all":[182],"ideals.":[188],"particular,":[190],"combinatorial":[193],"characterizations":[194],"Cohen-Macaulayness":[202],"$S/I_{c}(G)^{(k)}$":[204],"1$.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-20T00:00:00"}