{"id":"https://openalex.org/W4301329645","doi":"https://doi.org/10.48550/arxiv.1109.3462","title":"Picard-Fuchs equations of special one-parameter families of invertible polynomials","display_name":"Picard-Fuchs equations of special one-parameter families of invertible polynomials","publication_year":2011,"publication_date":"2011-09-15","ids":{"openalex":"https://openalex.org/W4301329645","doi":"https://doi.org/10.48550/arxiv.1109.3462"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1109.3462","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3462","pdf_url":"https://arxiv.org/pdf/1109.3462","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/1109.3462","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006432942","display_name":"Swantje G\u00e4hrs","orcid":"https://orcid.org/0000-0002-5851-3592","observed_orcids":["https://orcid.org/0000-0002-5851-3592"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"G\u00e4hrs, Swantje","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5006432942"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":10,"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":0.9951000213623047,"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":0.9951000213623047,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0010000000474974513,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.00039999998989515007,"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/picard-fuchs-equations","display_name":"Picard-Fuchs equations","score":0.9850000143051147},{"id":"https://openalex.org/keywords/invertible-polynomials","display_name":"invertible polynomials","score":0.9909999966621399},{"id":"https://openalex.org/keywords/one-parameter-families","display_name":"one-parameter families","score":0.8190000057220459},{"id":"https://openalex.org/keywords/period-integrals","display_name":"period integrals","score":0.8930000066757202},{"id":"https://openalex.org/keywords/hypersurfaces","display_name":"hypersurfaces","score":0.8579999804496765},{"id":"https://openalex.org/keywords/gkz-systems","display_name":"GKZ systems","score":0.9269999861717224},{"id":"https://openalex.org/keywords/poincare-series","display_name":"Poincar\u00e9 series","score":0.9819999933242798},{"id":"https://openalex.org/keywords/monodromy","display_name":"monodromy","score":0.972000002861023},{"id":"https://openalex.org/keywords/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.7149999737739563}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8792117834091187},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.8039216995239258},{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.7069664597511292},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5646023750305176},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5198705196380615},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4799549877643585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3422809839248657}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:1109.3462","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3462","pdf_url":"https://arxiv.org/pdf/1109.3462","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.1109.3462","doi":"https://doi.org/10.48550/arxiv.1109.3462","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1109.3462","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:1109.3462","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1109.3462","pdf_url":"https://arxiv.org/pdf/1109.3462","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4301329645.pdf","grobid_xml":"https://content.openalex.org/works/W4301329645.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2083163539","https://openalex.org/W2963450458","https://openalex.org/W2963487733","https://openalex.org/W7099831914"],"related_works":["https://openalex.org/W7096747272","https://openalex.org/W7155035605","https://openalex.org/W2021333695","https://openalex.org/W2135134285","https://openalex.org/W252400496","https://openalex.org/W4385575579","https://openalex.org/W188539903","https://openalex.org/W2337036084","https://openalex.org/W1964590419","https://openalex.org/W2609486550"],"abstract_inverted_index":{"The":[0],"thesis":[1],"deals":[2],"with":[3],"calculating":[4],"the":[5,24,31,34,44,48,56,60,63,67,76,80,93,97,100,103,107,110],"Picard-Fuchs":[6,45,68,101],"equation":[7,51,69],"of":[8,12,36,62,66,75,82,87,112],"special":[9],"one-parameter":[10],"families":[11,35],"invertible":[13,19],"polynomials.":[14],"In":[15],"particular,":[16],"for":[17],"an":[18],"polynomial":[20],"$g(x_1,...,x_n)$":[21],"we":[22,42,70,95],"consider":[23],"family":[25],"$f(x_1,...,x_n)=g(x_1,...,x_n)+s\\cdot\\prod":[26],"x_i$,":[27],"where":[28],"$s$":[29],"denotes":[30],"parameter.":[32],"For":[33,59],"hypersurfaces":[37],"defined":[38],"by":[39],"these":[40],"polynomials,":[41],"compute":[43],"equation,":[46,102],"i.e.":[47],"ordinary":[49],"differential":[50],"which":[52],"solutions":[53],"are":[54],"exactly":[55],"period":[57,113],"integrals.":[58,114],"proof":[61],"exact":[64],"appearance":[65],"use":[71],"a":[72],"combinatorial":[73],"version":[74],"Griffiths-Dwork":[77],"method":[78],"and":[79,90,106],"theory":[81],"\\GKZ":[83],"systems.":[84],"As":[85],"consequences":[86],"our":[88],"work":[89],"facts":[91],"from":[92],"literature,":[94],"show":[96],"relation":[98],"between":[99],"Poincar\u00e9":[104],"series":[105],"monodromy":[108],"in":[109],"space":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2022-10-05T00:00:00"}