{"id":"https://openalex.org/W7204870299","doi":"https://doi.org/10.48550/arxiv.2608.30236","title":"A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces","display_name":"A Note On the moduli space of rank two vector bundles on Hirzebruch surfaces","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204870299","doi":"https://doi.org/10.48550/arxiv.2608.30236"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30236","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30236","pdf_url":"https://arxiv.org/pdf/2608.30236","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/2608.30236","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085774662","display_name":"L. Roa-Leguizam\u00f3n","orcid":"https://orcid.org/0000-0002-3102-7674","observed_orcids":["https://orcid.org/0000-0002-3102-7674"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roa-Leguizam\u00f3n, L.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5085774662"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9980000257492065,"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":0.9980000257492065,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.00019999999494757503,"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/moduli-spaces-of-vector-bundles","display_name":"moduli of vector bundles","score":0.8669999837875366},{"id":"https://openalex.org/keywords/rank-2-vector-bundles","display_name":"rank 2 vector bundles","score":0.9660000205039978},{"id":"https://openalex.org/keywords/hirzebruch-surfaces","display_name":"Hirzebruch surfaces","score":0.9990000128746033},{"id":"https://openalex.org/keywords/chern-classes","display_name":"Chern classes","score":0.8140000104904175},{"id":"https://openalex.org/keywords/brill-noether-theory","display_name":"Brill-Noether theory","score":0.9670000076293945},{"id":"https://openalex.org/keywords/polarization-change","display_name":"polarization change","score":0.6579999923706055}],"concepts":[{"id":"https://openalex.org/C95857938","wikidata":"https://www.wikidata.org/wiki/Q658429","display_name":"Vector bundle","level":2,"score":0.9207000136375427},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.7949000000953674},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7814000248908997},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6482999920845032},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5787000060081482},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5252000093460083},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4803999960422516},{"id":"https://openalex.org/C2778134712","wikidata":"https://www.wikidata.org/wiki/Q1047307","display_name":"Bundle","level":2,"score":0.4729999899864197},{"id":"https://openalex.org/C144947467","wikidata":"https://www.wikidata.org/wiki/Q2397465","display_name":"Tautological line bundle","level":5,"score":0.41200000047683716},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3610999882221222},{"id":"https://openalex.org/C151527765","wikidata":"https://www.wikidata.org/wiki/Q1069818","display_name":"Chern class","level":2,"score":0.35749998688697815},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.33059999346733093},{"id":"https://openalex.org/C56907000","wikidata":"https://www.wikidata.org/wiki/Q1365548","display_name":"Principal bundle","level":3,"score":0.3249000012874603},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C137318105","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Direction vector","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.26750001311302185}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30236","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30236","pdf_url":"https://arxiv.org/pdf/2608.30236","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.2608.30236","doi":"https://doi.org/10.48550/arxiv.2608.30236","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30236","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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.30236","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30236","pdf_url":"https://arxiv.org/pdf/2608.30236","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/W7204870299.pdf","grobid_xml":"https://content.openalex.org/works/W7204870299.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W3010376583"],"related_works":["https://openalex.org/W3010376583","https://openalex.org/W7204814732","https://openalex.org/W2022239277","https://openalex.org/W2161414022","https://openalex.org/W7052635410","https://openalex.org/W2963377845","https://openalex.org/W2002274970","https://openalex.org/W2963955451","https://openalex.org/W2090640907","https://openalex.org/W7156162901"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,39,55,58,79],"this":[3],"paper":[4],"is":[5],"to":[6,29,68],"study":[7],"the":[8,36,56,59],"Segre":[9,37],"invariant":[10],"for":[11,81],"rank":[12,41,82],"$2$":[13,42,83],"vector":[14,43,84],"bundles":[15,85],"on":[16,45,86],"Hirzebruch":[17],"surfaces":[18],"$\\mathbb{F}_e$,":[19],"$e":[20],"\\geq":[21],"0$.":[22],"We":[23,51],"give":[24],"necessary":[25],"conditions":[26],"in":[27],"order":[28],"determine":[30],"what":[31],"numbers":[32],"can":[33],"appear":[34],"as":[35],"Invariant":[38],"a":[40,53],"bundle":[44],"$\\mathbb{F}_e$":[46],"with":[47],"fixed":[48],"Chern":[49],"classes.":[50],"compute":[52],"bound":[54],"dimensions":[57],"strata":[60],"whenever":[61],"are":[62],"non-empty.":[63],"Finally,":[64],"we":[65],"present":[66],"applications":[67],"Brill-Noether":[69],"Theory":[70],"and":[71],"describe":[72],"differences":[73],"between":[74],"moduli":[75],"spaces":[76],"under":[77],"change":[78],"polarization":[80],"$\\mathbb{F}_e$.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-02T00:00:00"}
