{"id":"https://openalex.org/W4416746751","doi":"https://doi.org/10.3390/math13233808","title":"On the Hilbert Function of Partially General Unions of Double Points","display_name":"On the Hilbert Function of Partially General Unions of Double Points","publication_year":2025,"publication_date":"2025-11-27","ids":{"openalex":"https://openalex.org/W4416746751","doi":"https://doi.org/10.3390/math13233808"},"language":"en","primary_location":{"id":"doi:10.3390/math13233808","doi":"https://doi.org/10.3390/math13233808","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math13233808","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/math13233808","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080462516","display_name":"Edoardo Ballico","orcid":"https://orcid.org/0000-0002-1432-7413","observed_orcids":["https://orcid.org/0000-0002-1432-7413"]},"institutions":[{"id":"https://openalex.org/I193223587","display_name":"University of Trento","ror":"https://ror.org/05trd4x28","country_code":"IT","type":"education","lineage":["https://openalex.org/I193223587"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Edoardo Ballico","raw_affiliation_strings":["Department of Mathematics, University of Trento, 38123 Trento, Italy"],"raw_orcid":"https://orcid.org/0000-0002-1432-7413","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Trento, 38123 Trento, Italy","institution_ids":["https://openalex.org/I193223587"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5080462516"],"corresponding_institution_ids":["https://openalex.org/I193223587"],"apc_list":{"value":2600,"currency":"CHF","value_usd":3137},"apc_paid":{"value":2600,"currency":"CHF","value_usd":3137},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.35996398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"23","first_page":"3808","last_page":"3808"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.8353999853134155,"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":0.8353999853134155,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.15929999947547913,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/hilbert-functions","display_name":"Hilbert functions","score":0.9959999918937683},{"id":"https://openalex.org/keywords/double-points","display_name":"double points","score":0.9679999947547913},{"id":"https://openalex.org/keywords/veronese-varieties","display_name":"Veronese varieties","score":0.9440000057220459},{"id":"https://openalex.org/keywords/segre-veronese-varieties","display_name":"Segre-Veronese varieties","score":0.9639999866485596},{"id":"https://openalex.org/keywords/projective-varieties","display_name":"projective varieties","score":0.3370000123977661}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8342000246047974},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6941999793052673},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.492900013923645},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4323999881744385},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.36039999127388},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3449999988079071},{"id":"https://openalex.org/C57033185","wikidata":"https://www.wikidata.org/wiki/Q5761236","display_name":"Hilbert series and Hilbert polynomial","level":3,"score":0.3434999883174896},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.32260000705718994},{"id":"https://openalex.org/C76103427","wikidata":"https://www.wikidata.org/wiki/Q5761197","display_name":"Hilbert R-tree","level":5,"score":0.29919999837875366},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2854999899864197},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.28519999980926514},{"id":"https://openalex.org/C3018216069","wikidata":"https://www.wikidata.org/wiki/Q5300062","display_name":"Double loop","level":2,"score":0.2833000123500824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27810001373291016},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.263700008392334}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/math13233808","doi":"https://doi.org/10.3390/math13233808","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math13233808","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c33d0fa27b7e4b8ea29a42bd193336b4","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/c33d0fa27b7e4b8ea29a42bd193336b4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics, Vol 13, Iss 23, p 3808 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/math13233808","doi":"https://doi.org/10.3390/math13233808","is_oa":true,"landing_page_url":"https://doi.org/10.3390/math13233808","pdf_url":null,"source":{"id":"https://openalex.org/S4210192031","display_name":"Mathematics","issn_l":"2227-7390","issn":["2227-7390"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1554656276","https://openalex.org/W1732649455","https://openalex.org/W1984263210","https://openalex.org/W2022694312","https://openalex.org/W2042825883","https://openalex.org/W2088376487","https://openalex.org/W2095850670","https://openalex.org/W2096735200","https://openalex.org/W2102892751","https://openalex.org/W2122026793","https://openalex.org/W2135925362","https://openalex.org/W2153603873","https://openalex.org/W2154013142","https://openalex.org/W2170325232","https://openalex.org/W2243807992","https://openalex.org/W2904001778","https://openalex.org/W2912135602","https://openalex.org/W2964076006","https://openalex.org/W3149460836","https://openalex.org/W4224260790","https://openalex.org/W4248269519","https://openalex.org/W4390638474","https://openalex.org/W4401047843","https://openalex.org/W4401329823","https://openalex.org/W4404562457","https://openalex.org/W4415059718"],"related_works":[],"abstract_inverted_index":{"We":[0,63],"study":[1,42],"the":[2,38,43,52],"Hilbert":[3],"function":[4],"of":[5,8,12,19,30,34,48,58,60,76],"a":[6,9,16,73],"union":[7],"fixed":[10],"set":[11],"double":[13,21,28,77],"points":[14,29],"and":[15,33,51],"prescribed":[17],"number":[18,75],"general":[20],"points.":[22,78],"Our":[23],"main":[24],"results":[25],"are":[26],"for":[27,72],"Veronese":[31],"varieties":[32],"Segre\u2013Veronese":[35,39],"varieties.":[36],"Among":[37],"varieties,":[40],"we":[41],"ones":[44,53],"with":[45,54,67],"all":[46],"factors":[47],"dimension":[49,61],"one":[50,57],"two":[55],"factors,":[56],"them":[59],"one.":[62],"give":[64],"many":[65],"examples":[66],"exceptional":[68],"or":[69],"controlled":[70],"behavior":[71],"small":[74]},"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-11-28T00:00:00"}