{"id":"https://openalex.org/W7204887217","doi":"https://doi.org/10.48550/arxiv.2608.29485","title":"The Picard number of fibred Mori dream surfaces","display_name":"The Picard number of fibred Mori dream surfaces","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7204887217","doi":"https://doi.org/10.48550/arxiv.2608.29485"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29485","pdf_url":"https://arxiv.org/pdf/2608.29485","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/2608.29485","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049899633","display_name":"Federico Fallucca","orcid":"https://orcid.org/0000-0003-4431-7838","observed_orcids":["https://orcid.org/0000-0003-4431-7838"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fallucca, Federico","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009824207","display_name":"Roberto Pignatelli","orcid":"https://orcid.org/0000-0002-1850-7577","observed_orcids":["https://orcid.org/0000-0002-1850-7577"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pignatelli, Roberto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086346057","display_name":"Francesco Polizzi","orcid":"https://orcid.org/0000-0002-9593-7626","observed_orcids":["https://orcid.org/0000-0002-9593-7626"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Polizzi, Francesco","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":0.9994999766349792,"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":0.0003000000142492354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mori-dream-spaces","display_name":"Mori dream spaces","score":0.8270000219345093},{"id":"https://openalex.org/keywords/picard-number","display_name":"Picard number","score":0.9760000109672546},{"id":"https://openalex.org/keywords/elliptic-fibrations","display_name":"elliptic fibrations","score":0.8840000033378601},{"id":"https://openalex.org/keywords/mordell-weil-group","display_name":"Mordell-Weil group","score":0.9819999933242798},{"id":"https://openalex.org/keywords/fermat-surfaces","display_name":"Fermat surfaces","score":0.9710000157356262},{"id":"https://openalex.org/keywords/algebraic-surfaces","display_name":"algebraic surfaces","score":0.5080000162124634}],"concepts":[{"id":"https://openalex.org/C54486226","wikidata":"https://www.wikidata.org/wiki/Q493941","display_name":"Fibration","level":3,"score":0.9319000244140625},{"id":"https://openalex.org/C133776654","wikidata":"https://www.wikidata.org/wiki/Q2381352","display_name":"Fibered knot","level":2,"score":0.8866000175476074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8324999809265137},{"id":"https://openalex.org/C2781095916","wikidata":"https://www.wikidata.org/wiki/Q36348","display_name":"Dream","level":2,"score":0.583299994468689},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5600000023841858},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5245000123977661},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5067999958992004},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3546999990940094},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.3546999990940094},{"id":"https://openalex.org/C159876591","wikidata":"https://www.wikidata.org/wiki/Q662830","display_name":"Fundamental group","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C519885992","wikidata":"https://www.wikidata.org/wiki/Q161","display_name":"Fiber","level":2,"score":0.32350000739097595},{"id":"https://openalex.org/C25534917","wikidata":"https://www.wikidata.org/wiki/Q1326955","display_name":"Exact sequence","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.2980000078678131},{"id":"https://openalex.org/C75280867","wikidata":"https://www.wikidata.org/wiki/Q877775","display_name":"Projective space","level":3,"score":0.29649999737739563},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.29350000619888306},{"id":"https://openalex.org/C3019735035","wikidata":"https://www.wikidata.org/wiki/Q2502381","display_name":"Smooth surface","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.2806999981403351},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C55232844","wikidata":"https://www.wikidata.org/wiki/Q1627604","display_name":"Hopf fibration","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29485","pdf_url":"https://arxiv.org/pdf/2608.29485","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.2608.29485","doi":"https://doi.org/10.48550/arxiv.2608.29485","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29485","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:2608.29485","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29485","pdf_url":"https://arxiv.org/pdf/2608.29485","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":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320334045","display_name":"Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni","ror":"https://ror.org/00b9dvn87"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204887217.pdf","grobid_xml":"https://content.openalex.org/works/W7204887217.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1520679147","https://openalex.org/W1522904849","https://openalex.org/W1552623250","https://openalex.org/W1973589162","https://openalex.org/W1979759507","https://openalex.org/W1983511768","https://openalex.org/W2001894015","https://openalex.org/W2013335670","https://openalex.org/W2042973772","https://openalex.org/W2052532747","https://openalex.org/W2066504038","https://openalex.org/W2091526610","https://openalex.org/W2143304250","https://openalex.org/W2326855965","https://openalex.org/W2769144620","https://openalex.org/W2944087681","https://openalex.org/W2963248418","https://openalex.org/W2963341514","https://openalex.org/W2963951194","https://openalex.org/W2964064536","https://openalex.org/W3104591055","https://openalex.org/W4256012969","https://openalex.org/W4294636789","https://openalex.org/W4384069138","https://openalex.org/W4385461476","https://openalex.org/W4405301217","https://openalex.org/W4410826965","https://openalex.org/W4414396121","https://openalex.org/W7202187917"],"related_works":["https://openalex.org/W7202187917","https://openalex.org/W2155736920","https://openalex.org/W7213436672","https://openalex.org/W2120358884","https://openalex.org/W4410453447","https://openalex.org/W3103913628","https://openalex.org/W2512331506","https://openalex.org/W1967168526","https://openalex.org/W1485578910","https://openalex.org/W2118415121"],"abstract_inverted_index":{"Let":[0],"$S$":[1,27,83],"be":[2,48],"a":[3,10,18,29,78,85,104,110,114,118],"smooth":[4,19],"complex":[5],"projective":[6,20],"surface":[7,111,147],"endowed":[8],"with":[9,77],"fibration":[11,71],"$f":[12,72],"\\colon":[13,73],"S":[14,74],"\\to":[15,75],"C$":[16],"onto":[17],"curve":[21,115],"$C$.":[22],"We":[23,122],"prove":[24],"that,":[25,67],"if":[26,36],"is":[28,40,66,84,98,103,116],"Mori":[30,86,119,155],"dream":[31,87,120,156],"space":[32],"(or,":[33],"more":[34],"generally,":[35],"its":[37],"pseudo-effective":[38],"cone":[39],"polyhedral)":[41],"then":[42],"the":[43,53,57,89,93,141],"Picard":[44],"number":[45],"$\u03c1(S)$":[46],"can":[47],"effectively":[49],"computed":[50],"by":[51,149],"counting":[52],"irreducible":[54],"components":[55],"of":[56,60,92,96,132],"reducible":[58],"fibres":[59],"$f$.":[61],"A":[62],"first":[63],"simple":[64,105],"consequence":[65],"given":[68],"an":[69],"elliptic":[70],"\\mathbb{P}^1$":[76],"section":[79],"and":[80,140,151],"such":[81],"that":[82,109,124],"space,":[88],"Mordell-Weil":[90],"group":[91],"general":[94],"fibre":[95],"$f$":[97],"finite.":[99],"The":[100],"main":[101],"application":[102],"criterion":[106],"for":[107],"proving":[108],"fibred":[112],"over":[113],"not":[117,154],"space.":[121],"show":[123],"certain":[125],"Horikawa":[126],"surfaces,":[127,139],"Fermat":[128],"surfaces":[129],"in":[130],"$\\mathbb{P}^{3}$":[131],"every":[133],"degree":[134],"$\\ge":[135],"4$,":[136],"particular":[137],"product-quotient":[138],"minimal":[142],"simply":[143],"connected":[144],"numerical":[145],"Godeaux":[146],"constructed":[148],"Craighero":[150],"Gattazzo":[152],"are":[153],"spaces.":[157]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}