{"id":"https://openalex.org/W7214948191","doi":"https://doi.org/10.48550/arxiv.2609.37936","title":"Dolbeault-Hochster Theory of Polytopal LVM Manifolds","display_name":"Dolbeault-Hochster Theory of Polytopal LVM Manifolds","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214948191","doi":"https://doi.org/10.48550/arxiv.2609.37936"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37936","pdf_url":"https://arxiv.org/pdf/2609.37936","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/2609.37936","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067549542","display_name":"Ludmil Vasilev Katzarkov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Katzarkov, Ludmil","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023373586","display_name":"Kyoung-Seog Lee","orcid":"https://orcid.org/0000-0003-3575-5238","observed_orcids":["https://orcid.org/0000-0003-3575-5238"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lee, Kyoung-Seog","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050447492","display_name":"Ernesto Lupercio","orcid":"https://orcid.org/0000-0002-7540-3416","observed_orcids":["https://orcid.org/0000-0002-7540-3416"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lupercio, Ernesto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083152352","display_name":"Laurent Meersseman","orcid":"https://orcid.org/0000-0003-2307-0944","observed_orcids":["https://orcid.org/0000-0003-2307-0944"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meersseman, Laurent","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/T12351","display_name":"Geometry and complex manifolds","score":0.8422999978065491,"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/T12351","display_name":"Geometry and complex manifolds","score":0.8422999978065491,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.14470000565052032,"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":0.00279999990016222,"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/dolbeault-cohomology","display_name":"Dolbeault cohomology","score":0.9490000009536743},{"id":"https://openalex.org/keywords/hodge-diamond","display_name":"Hodge diamond","score":0.9739999771118164},{"id":"https://openalex.org/keywords/kodaira-spencer-map","display_name":"Kodaira-Spencer map","score":0.9449999928474426},{"id":"https://openalex.org/keywords/holomorphic-families","display_name":"holomorphic families","score":0.47600001096725464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.926800012588501},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.6854000091552734},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6468999981880188},{"id":"https://openalex.org/C42448751","wikidata":"https://www.wikidata.org/wiki/Q855622","display_name":"Sectional curvature","level":4,"score":0.5683000087738037},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.5494999885559082},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5468000173568726},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4860000014305115},{"id":"https://openalex.org/C25534917","wikidata":"https://www.wikidata.org/wiki/Q1326955","display_name":"Exact sequence","level":2,"score":0.445499986410141},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.374099999666214},{"id":"https://openalex.org/C27602778","wikidata":"https://www.wikidata.org/wiki/Q578874","display_name":"Complex manifold","level":3,"score":0.37400001287460327},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.34769999980926514},{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.3434999883174896},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31369999051094055},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","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":0.28209999203681946},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2685999870300293},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C68365058","wikidata":"https://www.wikidata.org/wiki/Q1179446","display_name":"De Rham cohomology","level":4,"score":0.25850000977516174}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37936","pdf_url":"https://arxiv.org/pdf/2609.37936","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.2609.37936","doi":"https://doi.org/10.48550/arxiv.2609.37936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37936","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:2609.37936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37936","pdf_url":"https://arxiv.org/pdf/2609.37936","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/G2174268181","display_name":null,"funder_award_id":"DO1-239/10.12.2024","funder_id":"https://openalex.org/F4320323575","funder_display_name":"Bulgarian Academy of Sciences"}],"funders":[{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320323575","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214948191.pdf","grobid_xml":"https://content.openalex.org/works/W7214948191.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W78597518","https://openalex.org/W1515761639","https://openalex.org/W1626852528","https://openalex.org/W1637025518","https://openalex.org/W1952108362","https://openalex.org/W1984221802","https://openalex.org/W1988974064","https://openalex.org/W2013872671","https://openalex.org/W2024381970","https://openalex.org/W2024826432","https://openalex.org/W2048669464","https://openalex.org/W2060185552","https://openalex.org/W2072725522","https://openalex.org/W2090941457","https://openalex.org/W2092786894","https://openalex.org/W2096154319","https://openalex.org/W2103938537","https://openalex.org/W2137477478","https://openalex.org/W2314913022","https://openalex.org/W2329729431","https://openalex.org/W2460366081","https://openalex.org/W2884032501","https://openalex.org/W2942933964","https://openalex.org/W2962984051","https://openalex.org/W2963150729","https://openalex.org/W2963391876","https://openalex.org/W2963405439","https://openalex.org/W2964197354","https://openalex.org/W2967520749","https://openalex.org/W3092448084","https://openalex.org/W4244914147","https://openalex.org/W4300596011","https://openalex.org/W4400475829","https://openalex.org/W4404354489","https://openalex.org/W4409317639","https://openalex.org/W7077064847","https://openalex.org/W7162628936"],"related_works":["https://openalex.org/W7220893481","https://openalex.org/W2079163412","https://openalex.org/W635572296","https://openalex.org/W3005141968","https://openalex.org/W2951437331","https://openalex.org/W2076928428","https://openalex.org/W1965958553","https://openalex.org/W2779359014","https://openalex.org/W2888481967","https://openalex.org/W4396574284"],"abstract_inverted_index":{"We":[0,132,178],"compute":[1],"the":[2,19,28,31,45,59,65,69,73,79,114,119,124,128,150,180,184,203,205],"Dolbeault":[3,46,156],"cohomology":[4,53,157],"of":[5,30,51,55,58,72,121,155,183,213],"minimally":[6],"stable":[7],"polytopal":[8],"LVM":[9],"manifolds":[10],"using":[11],"a":[12,85,134,139,190,199,210,230],"finite":[13],"curvature":[14,32,80,99,125,146],"complex.":[15],"Let":[16],"$B$":[17],"be":[18],"indispensable":[20],"weight":[21,186],"block.":[22],"A":[23],"canonical":[24],"exact":[25],"sequence":[26],"identifies":[27],"kernel":[29],"map":[33,182,221],"with":[34,39,64,141,195],"$(\\operatorname{coker}B)^\\vee$":[35],"and":[36,82,95,123,188,216],"its":[37],"cokernel":[38],"$(\\ker":[40],"B)^\\vee$.":[41],"At":[42,162],"full":[43,163],"rank,":[44,164],"groups":[47,54],"are":[48],"direct":[49],"sums":[50],"reduced":[52],"induced":[56],"subcomplexes":[57],"visible":[60,143],"simplicial":[61],"sphere,":[62],"tensored":[63],"exterior":[66],"algebra":[67],"on":[68],"complex":[70],"dual":[71],"deck":[74],"lattice.":[75],"One":[76],"proof":[77],"uses":[78],"model":[81],"Stanley--Reisner":[83],"Tor;":[84],"second":[86],"gives":[87],"an":[88],"additive":[89],"comparison":[90],"through":[91],"completed":[92],"Laurent":[93],"expansions":[94],"holomorphic":[96,136,165,231],"descent.":[97],"Full":[98],"rank":[100,126,147],"is":[101,222],"equivalent":[102],"to":[103],"Frolicher":[104],"degeneration":[105],"at":[106,149],"$E_1$.":[107],"Every":[108],"manifold":[109],"in":[110,174,229],"this":[111],"class":[112,227],"fails":[113],"$\\partial\\bar\\partial$":[115],"lemma.":[116],"For":[117,198],"polygons,":[118],"number":[120],"facets":[122],"determine":[127,179],"entire":[129],"Hodge":[130],"diamond.":[131],"construct":[133],"proper":[135],"family":[137,187],"over":[138,202],"disk":[140],"fixed":[142],"square":[144],"whose":[145],"drops":[148],"origin.":[151],"The":[152,218,224],"total":[153],"dimension":[154],"increases":[158],"there":[159],"by":[160],"sixteen.":[161],"descent":[166],"also":[167],"computes":[168],"tangent-sheaf":[169],"cohomology,":[170],"including":[171],"resonant":[172,200],"contributions":[173],"positive":[175],"Cech":[176,226],"degree.":[177],"Kodaira--Spencer":[181],"normalized":[185],"give":[189],"cohomological":[191],"criterion":[192],"for":[193],"semiuniversality":[194],"smooth":[196],"base.":[197],"example":[201],"square,":[204],"global":[206],"vector":[207],"fields":[208],"have":[209],"polynomial":[211],"basis":[212],"nine":[214],"elements":[215],"$h^1(\u0398)=19$.":[217],"primary":[219],"obstruction":[220],"nonzero.":[223],"additional":[225],"integrates":[228],"family.":[232]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}