{"id":"https://openalex.org/W2079685734","doi":"https://doi.org/10.1090/s0025-5718-06-01853-9","title":"The group of Weierstrass points of a plane quartic with at least eight hyperflexes","display_name":"The group of Weierstrass points of a plane quartic with at least eight hyperflexes","publication_year":2006,"publication_date":"2006-05-01","ids":{"openalex":"https://openalex.org/W2079685734","doi":"https://doi.org/10.1090/s0025-5718-06-01853-9","mag":"2079685734"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-06-01853-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01853-9","pdf_url":"https://www.ams.org/mcom/2006-75-255/S0025-5718-06-01853-9/S0025-5718-06-01853-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-255/S0025-5718-06-01853-9/S0025-5718-06-01853-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031170235","display_name":"Martine Girard","orcid":null},"institutions":[{"id":"https://openalex.org/I121797337","display_name":"Leiden University","ror":"https://ror.org/027bh9e22","country_code":"NL","type":"education","lineage":["https://openalex.org/I121797337"]},{"id":"https://openalex.org/I129604602","display_name":"The University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU","NL"],"is_corresponding":true,"raw_author_name":"Martine Girard","raw_affiliation_strings":["School of Mathematics and Statistics, The University of Sydney, New South Wales, NSW 2006, Australia","Universiteit Leiden, Mathematisch Instituut, 2300 R. A. Leiden, The Netherlands"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of Sydney, New South Wales, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"Universiteit Leiden, Mathematisch Instituut, 2300 R. A. Leiden, The Netherlands","institution_ids":["https://openalex.org/I121797337"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5031170235"],"corresponding_institution_ids":["https://openalex.org/I121797337","https://openalex.org/I129604602"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.14932033,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"75","issue":"255","first_page":"1561","last_page":"1583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9865000247955322,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9811999797821045,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.891838550567627},{"id":"https://openalex.org/keywords/moduli-space","display_name":"Moduli space","score":0.8424728512763977},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.8134530782699585},{"id":"https://openalex.org/keywords/quartic-plane-curve","display_name":"Quartic plane curve","score":0.7996950149536133},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5683668851852417},{"id":"https://openalex.org/keywords/quartic-surface","display_name":"Quartic surface","score":0.5332474708557129},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5327575206756592},{"id":"https://openalex.org/keywords/moduli-of-algebraic-curves","display_name":"Moduli of algebraic curves","score":0.5065597295761108},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.49089986085891724},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4791123867034912},{"id":"https://openalex.org/keywords/weierstrass-functions","display_name":"Weierstrass functions","score":0.4463024139404297},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4396651089191437},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.4233267307281494},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.12740537524223328}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.891838550567627},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.8424728512763977},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.8134530782699585},{"id":"https://openalex.org/C84181032","wikidata":"https://www.wikidata.org/wiki/Q1857574","display_name":"Quartic plane curve","level":3,"score":0.7996950149536133},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5683668851852417},{"id":"https://openalex.org/C117139701","wikidata":"https://www.wikidata.org/wiki/Q7269363","display_name":"Quartic surface","level":3,"score":0.5332474708557129},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5327575206756592},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.5065597295761108},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.49089986085891724},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4791123867034912},{"id":"https://openalex.org/C65945562","wikidata":"https://www.wikidata.org/wiki/Q3075283","display_name":"Weierstrass functions","level":2,"score":0.4463024139404297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4396651089191437},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.4233267307281494},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.12740537524223328},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-06-01853-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01853-9","pdf_url":"https://www.ams.org/mcom/2006-75-255/S0025-5718-06-01853-9/S0025-5718-06-01853-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.192.4911","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.4911","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/journals/mcom/2006-75-255/S0025-5718-06-01853-9/S0025-5718-06-01853-9.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-06-01853-9","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-06-01853-9","pdf_url":"https://www.ams.org/mcom/2006-75-255/S0025-5718-06-01853-9/S0025-5718-06-01853-9.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2079685734.pdf","grobid_xml":"https://content.openalex.org/works/W2079685734.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W71358917","https://openalex.org/W178528876","https://openalex.org/W859353257","https://openalex.org/W1516318957","https://openalex.org/W1534976569","https://openalex.org/W1586175698","https://openalex.org/W1987144829","https://openalex.org/W1987648105","https://openalex.org/W2018862968","https://openalex.org/W2064832150","https://openalex.org/W2092461368","https://openalex.org/W2169281434","https://openalex.org/W4248974416","https://openalex.org/W6631935881"],"related_works":["https://openalex.org/W2952119375","https://openalex.org/W4299790380","https://openalex.org/W1488340099","https://openalex.org/W2324830980","https://openalex.org/W1972667525","https://openalex.org/W1524267494","https://openalex.org/W2963611704","https://openalex.org/W2036870198","https://openalex.org/W1582119139","https://openalex.org/W2950695782"],"abstract_inverted_index":{"The":[0],"group":[1,24,61],"generated":[2],"by":[3],"the":[4,19,53,56,73],"Weierstrass":[5,35],"points":[6,36],"of":[7,18,43,59,70,103,105],"a":[8,63,67],"smooth":[9,27],"curve":[10],"in":[11,72],"its":[12],"Jacobian":[13],"is":[14],"an":[15,46],"intrinsic":[16],"invariant":[17],"curve.":[20],"We":[21],"determine":[22],"this":[23,60],"for":[25,62],"all":[26],"quartics":[28],"with":[29],"eight":[30],"hyperflexes":[31,71],"or":[32],"more.":[33],"Since":[34],"are":[37],"closely":[38],"related":[39],"to":[40],"moduli":[41,74],"spaces":[42],"curves,":[44],"as":[45],"application,":[47],"we":[48],"get":[49],"bounds":[50],"on":[51],"both":[52],"rank":[54],"and":[55],"torsion":[57],"part":[58],"generic":[64],"quartic":[65],"having":[66],"fixed":[68],"number":[69],"space":[75],"<inline-formula":[76],"content-type=\"math/mathml\">":[77],"<mml:math":[78],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[79],"alttext=\"script":[80],"upper":[81],"M":[82],"3\">":[83],"<mml:semantics>":[84],"<mml:msub>":[85],"<mml:mrow":[86,92],"class=\"MJX-TeXAtom-ORD\">":[87,93],"<mml:mi":[88],"class=\"MJX-tex-caligraphic\"":[89],"mathvariant=\"script\">M</mml:mi>":[90],"</mml:mrow>":[91,95],"<mml:mn>3</mml:mn>":[94],"</mml:msub>":[96],"<mml:annotation":[97],"encoding=\"application/x-tex\">\\mathcal":[98],"{M}_{3}</mml:annotation>":[99],"</mml:semantics>":[100],"</mml:math>":[101],"</inline-formula>":[102],"curves":[104],"genus":[106],"3.":[107]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-22T06:01:30.510260","created_date":"2025-10-10T00:00:00"}
