Mori dream spaces and birational rigidity of Fano 3-folds

Name: Work Video:
Duration: 3 min 30 s
Description: We highlight a relation between the existence of Sarkisov links and the finite generation of (certain) Cox rings. We introduce explicit methods to use this relation in order to prove birational rigidity statements. To illustrate, we complete the birational rigidity results of Okada for Fano complete intersection 3-folds in singular weighted projective spaces.
Hamid Ahmadinezhad; Francesco Zucconi
{'id': 'https://openalex.org/W2953044371', 'doi': None, 'title': 'Mori dream spaces and birational rigidity of Fano 3-folds', 'display_name': 'Mori dream spaces and birational rigidity of Fano 3-folds', 'publication_year': 2014, 'publication_date': '2014-07-14', 'ids': {'openalex': 'https://openalex.org/W2953044371', 'mag': '2953044371'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://arxiv.org/pdf/1407.3724v2', 'pdf_url': None, '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}, 'type': 'preprint', 'type_crossref': 'posted-content', 'indexed_in': [], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5108402687', 'display_name': 'Hamid Ahmadinezhad', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I36234482', 'display_name': 'University of Bristol', 'ror': 'https://ror.org/0524sp257', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I36234482']}], 'countries': ['GB'], 'is_corresponding': False, 'raw_author_name': 'Hamid Ahmadinezhad', 'raw_affiliation_strings': ['School of Mathematics, University of Bristol,    Bristol BS8 1TW, UK'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematics, University of Bristol,    Bristol BS8 1TW, UK', 'institution_ids': ['https://openalex.org/I36234482']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5065148708', 'display_name': 'Francesco Zucconi', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I129043915', 'display_name': 'University of Udine', 'ror': 'https://ror.org/05ht0mh31', 'country_code': 'IT', 'type': 'education', 'lineage': ['https://openalex.org/I129043915']}], 'countries': ['IT'], 'is_corresponding': False, 'raw_author_name': 'Francesco Zucconi', 'raw_affiliation_strings': ['Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Via delle Scienze 206, 33100, Udine, Italy,'], 'affiliations': [{'raw_affiliation_string': 'Dipartimento di Matematica e Informatica, Università degli Studi di Udine, Via delle Scienze 206, 33100, Udine, Italy,', 'institution_ids': ['https://openalex.org/I129043915']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': None, 'has_fulltext': False, 'cited_by_count': 1, 'citation_normalized_percentile': {'value': 0.580032, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 66, 'max': 73}, 'biblio': {'volume': None, 'issue': None, 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9999, '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': 0.9999, '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': 0.9997, '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/T11680', 'display_name': 'Advanced Algebra and Geometry', 'score': 0.9985, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, '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': 0.9438028}, {'id': 'https://openalex.org/keywords/rigidity', 'display_name': 'Rigidity (electromagnetism)', 'score': 0.9014888}, {'id': 'https://openalex.org/keywords/birational-geometry', 'display_name': 'Birational Geometry', 'score': 0.4303629}], 'concepts': [{'id': 'https://openalex.org/C39757861', 'wikidata': 'https://www.wikidata.org/wiki/Q1395814', 'display_name': 'Fano plane', 'level': 2, 'score': 0.9438028}, {'id': 'https://openalex.org/C160343418', 'wikidata': 'https://www.wikidata.org/wiki/Q185256', 'display_name': 'Rigidity (electromagnetism)', 'level': 2, 'score': 0.9014888}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.66411877}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.6534867}, {'id': 'https://openalex.org/C96881808', 'wikidata': 'https://www.wikidata.org/wiki/Q1879333', 'display_name': 'Birational geometry', 'level': 2, 'score': 0.4303629}, {'id': 'https://openalex.org/C25343380', 'wikidata': 'https://www.wikidata.org/wiki/Q277521', 'display_name': 'Relation (database)', 'level': 2, 'score': 0.42966706}, {'id': 'https://openalex.org/C64543145', 'wikidata': 'https://www.wikidata.org/wiki/Q162942', 'display_name': 'Intersection (aeronautics)', 'level': 2, 'score': 0.421943}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.1613206}, {'id': 'https://openalex.org/C66938386', 'wikidata': 'https://www.wikidata.org/wiki/Q633538', 'display_name': 'Structural engineering', 'level': 1, 'score': 0.058552414}, {'id': 'https://openalex.org/C127413603', 'wikidata': 'https://www.wikidata.org/wiki/Q11023', 'display_name': 'Engineering', 'level': 0, 'score': 0.051784396}, {'id': 'https://openalex.org/C77088390', 'wikidata': 'https://www.wikidata.org/wiki/Q8513', 'display_name': 'Database', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C146978453', 'wikidata': 'https://www.wikidata.org/wiki/Q3798668', 'display_name': 'Aerospace engineering', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://arxiv.org/pdf/1407.3724v2', 'pdf_url': None, '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}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 19, 'referenced_works': ['https://openalex.org/W1568303740', 'https://openalex.org/W1592392589', 'https://openalex.org/W1661748376', 'https://openalex.org/W1965582960', 'https://openalex.org/W2008946915', 'https://openalex.org/W2021540843', 'https://openalex.org/W2055695318', 'https://openalex.org/W2069325370', 'https://openalex.org/W2090588358', 'https://openalex.org/W2135262512', 'https://openalex.org/W2162742210', 'https://openalex.org/W2318546049', 'https://openalex.org/W2573912247', 'https://openalex.org/W2951118845', 'https://openalex.org/W2964006748', 'https://openalex.org/W3098562814', 'https://openalex.org/W3098736869', 'https://openalex.org/W3101566580', 'https://openalex.org/W3124776382'], 'related_works': ['https://openalex.org/W595335887', 'https://openalex.org/W3107958605', 'https://openalex.org/W3099701691', 'https://openalex.org/W3023651066', 'https://openalex.org/W2964190517', 'https://openalex.org/W2964003646', 'https://openalex.org/W2952713851', 'https://openalex.org/W2951321768', 'https://openalex.org/W2949143348', 'https://openalex.org/W2900491350', 'https://openalex.org/W2794353296', 'https://openalex.org/W2437179053', 'https://openalex.org/W2333497261', 'https://openalex.org/W2272565781', 'https://openalex.org/W2036666078', 'https://openalex.org/W2014966200', 'https://openalex.org/W2009690456', 'https://openalex.org/W2007881425', 'https://openalex.org/W1481805736', 'https://openalex.org/W1126904971'], 'abstract_inverted_index': {'We': [0, 18], 'highlight': [1], 'a': [2], 'relation': [3, 25], 'between': [4], 'the': [5, 11, 37], 'existence': [6], 'of': [7, 14, 41], 'Sarkisov': [8], 'links': [9], 'and': [10], 'finite': [12], 'generation': [13], '(certain)': [15], 'Cox': [16], 'rings.': [17], 'introduce': [19], 'explicit': [20], 'methods': [21], 'to': [22, 28], 'use': [23], 'this': [24], 'in': [26, 48], 'order': [27], 'prove': [29], 'birational': [30, 38], 'rigidity': [31, 39], 'statements.': [32], 'To': [33], 'illustrate,': [34], 'we': [35], 'complete': [36, 45], 'results': [40], 'Okada': [42], 'for': [43], 'Fano': [44], 'intersection': [46], '3-folds': [47], 'singular': [49], 'weighted': [50], 'projective': [51], 'spaces.': [52]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2953044371', 'counts_by_year': [{'year': 2017, 'cited_by_count': 1}], 'updated_date': '2024-12-21T10:55:30.093122', 'created_date': '2019-06-27'}
Publication Information

Basic Information

Access and Citation

AI Researcher Chatbot

Primary Location

Authors

Topics

Keywords

Related Works
