Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W3105624962', 'doi': 'https://doi.org/10.3934/era.2011.18.131', 'title': 'Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes', 'display_name': 'Semisimplicity of the quantum cohomology for smooth Fano toric varieties associated with facet symmetric polytopes', 'publication_year': 2011, 'publication_date': '2011-09-01', 'ids': {'openalex': 'https://openalex.org/W3105624962', 'doi': 'https://doi.org/10.3934/era.2011.18.131', 'mag': '3105624962'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.3934/era.2011.18.131', 'pdf_url': 'https://www.aimsciences.org/data/article/export-pdf?id=707c1b18-deb8-46ba-a5e1-d36bbc3dbbcc', 'source': {'id': 'https://openalex.org/S118659917', 'display_name': 'Electronic Research Announcements', 'issn_l': '1935-9179', 'issn': ['1935-9179'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315844', 'host_organization_name': 'American Institute of Mathematical Sciences', 'host_organization_lineage': ['https://openalex.org/P4310315844'], 'host_organization_lineage_names': ['American Institute of Mathematical Sciences'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://www.aimsciences.org/data/article/export-pdf?id=707c1b18-deb8-46ba-a5e1-d36bbc3dbbcc', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5000794466', 'display_name': 'Maksim Maydanskiy', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I63966007', 'display_name': 'Massachusetts Institute of Technology', 'ror': 'https://ror.org/042nb2s44', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I63966007']}, {'id': 'https://openalex.org/I32971472', 'display_name': 'Yale University', 'ror': 'https://ror.org/03v76x132', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I32971472']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Maksim Maydanskiy', 'raw_affiliation_strings': ['Yale University, Mathematics Department, PO Box 208283, New Haven, Connecticut 06520, USA', 'the Mas-sachusetts Institute of Technology,'], 'affiliations': [{'raw_affiliation_string': 'the Mas-sachusetts Institute of Technology,', 'institution_ids': ['https://openalex.org/I63966007']}, {'raw_affiliation_string': 'Yale University, Mathematics Department, PO Box 208283, New Haven, Connecticut 06520, USA', 'institution_ids': ['https://openalex.org/I32971472']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5019199335', 'display_name': 'Benjamin P. Mirabelli', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I63966007', 'display_name': 'Massachusetts Institute of Technology', 'ror': 'https://ror.org/042nb2s44', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I63966007']}, {'id': 'https://openalex.org/I32971472', 'display_name': 'Yale University', 'ror': 'https://ror.org/03v76x132', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I32971472']}], 'countries': ['US'], 'is_corresponding': False, 'raw_author_name': 'Benjamin P. Mirabelli', 'raw_affiliation_strings': ['Yale University, Mathematics Department, PO Box 208283, New Haven, Connecticut 06520, USA', 'the Mas-sachusetts Institute of Technology,'], 'affiliations': [{'raw_affiliation_string': 'the Mas-sachusetts Institute of Technology,', 'institution_ids': ['https://openalex.org/I63966007']}, {'raw_affiliation_string': 'Yale University, Mathematics Department, PO Box 208283, New Haven, Connecticut 06520, USA', 'institution_ids': ['https://openalex.org/I32971472']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 0.556, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 2, 'citation_normalized_percentile': {'value': 0.413997, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 72, 'max': 76}, 'biblio': {'volume': '18', 'issue': '0', 'first_page': '131', 'last_page': '143'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10304', 'display_name': 'Geometric and Algebraic Topology', 'score': 0.9985, '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/T10304', 'display_name': 'Geometric and Algebraic Topology', 'score': 0.9985, '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/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9982, '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': 0.998, '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/fano-plane', 'display_name': 'Fano plane', 'score': 0.69659966}, {'id': 'https://openalex.org/keywords/dual-polyhedron', 'display_name': 'Dual polyhedron', 'score': 0.5352486}, {'id': 'https://openalex.org/keywords/superpotential', 'display_name': 'Superpotential', 'score': 0.4970918}, {'id': 'https://openalex.org/keywords/facet', 'display_name': 'Facet (psychology)', 'score': 0.46399873}], 'concepts': [{'id': 'https://openalex.org/C145691206', 'wikidata': 'https://www.wikidata.org/wiki/Q747980', 'display_name': 'Polytope', 'level': 2, 'score': 0.8323498}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7324517}, {'id': 'https://openalex.org/C39757861', 'wikidata': 'https://www.wikidata.org/wiki/Q1395814', 'display_name': 'Fano plane', 'level': 2, 'score': 0.69659966}, {'id': 'https://openalex.org/C136660716', 'wikidata': 'https://www.wikidata.org/wiki/Q7269022', 'display_name': 'Quantum cohomology', 'level': 4, 'score': 0.62807417}, {'id': 'https://openalex.org/C105313907', 'wikidata': 'https://www.wikidata.org/wiki/Q1053857', 'display_name': 'Dual polyhedron', 'level': 2, 'score': 0.5352486}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.5181014}, {'id': 'https://openalex.org/C168948012', 'wikidata': 'https://www.wikidata.org/wiki/Q3978010', 'display_name': 'Superpotential', 'level': 3, 'score': 0.4970918}, {'id': 'https://openalex.org/C43122875', 'wikidata': 'https://www.wikidata.org/wiki/Q5428522', 'display_name': 'Facet (psychology)', 'level': 4, 'score': 0.46399873}, {'id': 'https://openalex.org/C168619227', 'wikidata': 'https://www.wikidata.org/wiki/Q2190991', 'display_name': 'Symplectic geometry', 'level': 2, 'score': 0.4541707}, {'id': 'https://openalex.org/C72319582', 'wikidata': 'https://www.wikidata.org/wiki/Q584304', 'display_name': 'Degenerate energy levels', 'level': 2, 'score': 0.41589448}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.36677533}, {'id': 'https://openalex.org/C78606066', 'wikidata': 'https://www.wikidata.org/wiki/Q1198376', 'display_name': 'Cohomology', 'level': 2, 'score': 0.3531264}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.17792115}, {'id': 'https://openalex.org/C72738302', 'wikidata': 'https://www.wikidata.org/wiki/Q5384738', 'display_name': 'Equivariant cohomology', 'level': 3, 'score': 0.15719166}, {'id': 'https://openalex.org/C37914503', 'wikidata': 'https://www.wikidata.org/wiki/Q156495', 'display_name': 'Mathematical physics', 'level': 1, 'score': 0.14013296}, {'id': 'https://openalex.org/C62520636', 'wikidata': 'https://www.wikidata.org/wiki/Q944', 'display_name': 'Quantum mechanics', 'level': 1, 'score': 0.12093845}, {'id': 'https://openalex.org/C77805123', 'wikidata': 'https://www.wikidata.org/wiki/Q161272', 'display_name': 'Social psychology', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C15744967', 'wikidata': 'https://www.wikidata.org/wiki/Q9418', 'display_name': 'Psychology', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C187288502', 'wikidata': 'https://www.wikidata.org/wiki/Q641118', 'display_name': 'Personality', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C116674579', 'wikidata': 'https://www.wikidata.org/wiki/Q193442', 'display_name': 'Supersymmetry', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C2865642', 'wikidata': 'https://www.wikidata.org/wiki/Q378132', 'display_name': 'Big Five personality traits', 'level': 3, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.3934/era.2011.18.131', 'pdf_url': 'https://www.aimsciences.org/data/article/export-pdf?id=707c1b18-deb8-46ba-a5e1-d36bbc3dbbcc', 'source': {'id': 'https://openalex.org/S118659917', 'display_name': 'Electronic Research Announcements', 'issn_l': '1935-9179', 'issn': ['1935-9179'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315844', 'host_organization_name': 'American Institute of Mathematical Sciences', 'host_organization_lineage': ['https://openalex.org/P4310315844'], 'host_organization_lineage_names': ['American Institute of Mathematical Sciences'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'http://arxiv.org/abs/1103.0762', 'pdf_url': 'http://arxiv.org/pdf/1103.0762', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': None, 'pdf_url': 'http://arxiv.org/pdf/1103.0762.pdf', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/1103.0762', 'pdf_url': 'https://arxiv.org/pdf/1103.0762', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1103.0762', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.3934/era.2011.18.131', 'pdf_url': 'https://www.aimsciences.org/data/article/export-pdf?id=707c1b18-deb8-46ba-a5e1-d36bbc3dbbcc', 'source': {'id': 'https://openalex.org/S118659917', 'display_name': 'Electronic Research Announcements', 'issn_l': '1935-9179', 'issn': ['1935-9179'], 'is_oa': True, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315844', 'host_organization_name': 'American Institute of Mathematical Sciences', 'host_organization_lineage': ['https://openalex.org/P4310315844'], 'host_organization_lineage_names': ['American Institute of Mathematical Sciences'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W1995198937', 'https://openalex.org/W3105624962'], 'referenced_works_count': 19, 'referenced_works': ['https://openalex.org/W1519907557', 'https://openalex.org/W1521877949', 'https://openalex.org/W1522101460', 'https://openalex.org/W1563175314', 'https://openalex.org/W1611427702', 'https://openalex.org/W1651555256', 'https://openalex.org/W196954758', 'https://openalex.org/W1976521126', 'https://openalex.org/W2015438979', 'https://openalex.org/W2040968990', 'https://openalex.org/W2074378273', 'https://openalex.org/W2108840390', 'https://openalex.org/W2136480649', 'https://openalex.org/W2609373516', 'https://openalex.org/W3104930935', 'https://openalex.org/W4248269519', 'https://openalex.org/W4390632229', 'https://openalex.org/W4394642331', 'https://openalex.org/W596713504'], 'related_works': ['https://openalex.org/W4300895258', 'https://openalex.org/W4288093261', 'https://openalex.org/W3103454236', 'https://openalex.org/W3047821054', 'https://openalex.org/W2952999609', 'https://openalex.org/W2951812514', 'https://openalex.org/W2429044630', 'https://openalex.org/W1965410039', 'https://openalex.org/W1704977233', 'https://openalex.org/W1625610113'], 'abstract_inverted_index': {'The': [0], 'degree': [1], 'zero': [2], 'part': [3], 'of': [4, 9, 23, 38, 48], 'the': [5, 19, 45], 'quantum': [6], 'cohomology': [7], 'algebra': [8, 30], 'a': [10, 36], 'smooth': [11, 63], 'Fano': [12, 64], 'toric': [13, 65], 'symplectic': [14], 'manifold': [15], 'is': [16, 31], 'determined': [17], 'by': [18], 'superpotential': [20], 'function,': [21], 'W,': [22], 'its': [24], 'moment': [25, 71], 'polytope.': [26], 'In': [27, 52], 'particular,': [28], 'this': [29, 53, 58], 'semisimple,': [32], 'i.e.': [33], 'splits': [34], 'as': [35], 'product': [37], 'fields,': [39], 'if': [40, 43], 'and': [41], 'only': [42], 'all': [44, 62], 'critical': [46], 'points': [47], 'W': [49], 'are': [50], 'non-degenerate.': [51], 'paper': [54], 'we': [55], 'prove': [56], 'that': [57], 'non-degeneracy': [59], 'holds': [60], 'for': [61], 'varieties': [66], 'with': [67], 'facet-symmetric': [68], 'duals': [69], 'to': [70], 'polytopes.': [72]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3105624962', 'counts_by_year': [{'year': 2014, 'cited_by_count': 1}, {'year': 2012, 'cited_by_count': 1}], 'updated_date': '2024-12-11T18:15:37.220701', 'created_date': '2020-11-23'}