On Ziegler's conjectures for logarithmic derivations of arrangements Article Swipe
Takuro Abe
,
Graham Denham
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2307.08173
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2307.08173
In his paper and thesis in 1989, Ziegler posed several conjectures regarding commutative algebra related to hyperplane arrangements. In this article, we revisit two of them. One is on generic cuts of free arrangements, and the other has to do with minimal degree generators for the logarithmic differential forms. We prove the first one, and disprove the second one. We also give some positive answers to related problems he posed, using recent developments in arrangement theory.
Related Topics
Concepts
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2307.08173
- https://arxiv.org/pdf/2307.08173
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4384644651
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4384644651Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2307.08173Digital Object Identifier
- Title
-
On Ziegler's conjectures for logarithmic derivations of arrangementsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-07-16Full publication date if available
- Authors
-
Takuro Abe, Graham DenhamList of authors in order
- Landing page
-
https://arxiv.org/abs/2307.08173Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2307.08173Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2307.08173Direct OA link when available
- Concepts
-
Hyperplane, Mathematics, Logarithm, Degree (music), Commutative property, Algebra over a field, Differential (mechanical device), Pure mathematics, Combinatorics, Mathematical analysis, Engineering, Physics, Aerospace engineering, AcousticsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4384644651 |
|---|---|
| doi | https://doi.org/10.48550/arxiv.2307.08173 |
| ids.doi | https://doi.org/10.48550/arxiv.2307.08173 |
| ids.openalex | https://openalex.org/W4384644651 |
| fwci | |
| type | preprint |
| title | On Ziegler's conjectures for logarithmic derivations of arrangements |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T12812 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9819999933242798 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2604 |
| topics[0].subfield.display_name | Applied Mathematics |
| topics[0].display_name | Meromorphic and Entire Functions |
| topics[1].id | https://openalex.org/T12396 |
| topics[1].field.id | https://openalex.org/fields/26 |
| topics[1].field.display_name | Mathematics |
| topics[1].score | 0.9817000031471252 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2608 |
| topics[1].subfield.display_name | Geometry and Topology |
| topics[1].display_name | Advanced Differential Equations and Dynamical Systems |
| topics[2].id | https://openalex.org/T11428 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9667999744415283 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2602 |
| topics[2].subfield.display_name | Algebra and Number Theory |
| topics[2].display_name | Advanced Mathematical Identities |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C68693459 |
| concepts[0].level | 2 |
| concepts[0].score | 0.8628135919570923 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q657586 |
| concepts[0].display_name | Hyperplane |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.7232621312141418 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C39927690 |
| concepts[2].level | 2 |
| concepts[2].score | 0.7178984880447388 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q11197 |
| concepts[2].display_name | Logarithm |
| concepts[3].id | https://openalex.org/C2775997480 |
| concepts[3].level | 2 |
| concepts[3].score | 0.6014289855957031 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q586277 |
| concepts[3].display_name | Degree (music) |
| concepts[4].id | https://openalex.org/C183778304 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5679284334182739 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q165474 |
| concepts[4].display_name | Commutative property |
| concepts[5].id | https://openalex.org/C136119220 |
| concepts[5].level | 2 |
| concepts[5].score | 0.5165099501609802 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q1000660 |
| concepts[5].display_name | Algebra over a field |
| concepts[6].id | https://openalex.org/C93226319 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4694882035255432 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q193137 |
| concepts[6].display_name | Differential (mechanical device) |
| concepts[7].id | https://openalex.org/C202444582 |
| concepts[7].level | 1 |
| concepts[7].score | 0.4667380750179291 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q837863 |
| concepts[7].display_name | Pure mathematics |
| concepts[8].id | https://openalex.org/C114614502 |
| concepts[8].level | 1 |
| concepts[8].score | 0.24444594979286194 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q76592 |
| concepts[8].display_name | Combinatorics |
| concepts[9].id | https://openalex.org/C134306372 |
| concepts[9].level | 1 |
| concepts[9].score | 0.10000213980674744 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[9].display_name | Mathematical analysis |
| concepts[10].id | https://openalex.org/C127413603 |
| concepts[10].level | 0 |
| concepts[10].score | 0.0534881055355072 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q11023 |
| concepts[10].display_name | Engineering |
| concepts[11].id | https://openalex.org/C121332964 |
| concepts[11].level | 0 |
| concepts[11].score | 0.04966050386428833 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[11].display_name | Physics |
| concepts[12].id | https://openalex.org/C146978453 |
| concepts[12].level | 1 |
| concepts[12].score | 0.0 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q3798668 |
| concepts[12].display_name | Aerospace engineering |
| concepts[13].id | https://openalex.org/C24890656 |
| concepts[13].level | 1 |
| concepts[13].score | 0.0 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q82811 |
| concepts[13].display_name | Acoustics |
| keywords[0].id | https://openalex.org/keywords/hyperplane |
| keywords[0].score | 0.8628135919570923 |
| keywords[0].display_name | Hyperplane |
| keywords[1].id | https://openalex.org/keywords/mathematics |
| keywords[1].score | 0.7232621312141418 |
| keywords[1].display_name | Mathematics |
| keywords[2].id | https://openalex.org/keywords/logarithm |
| keywords[2].score | 0.7178984880447388 |
| keywords[2].display_name | Logarithm |
| keywords[3].id | https://openalex.org/keywords/degree |
| keywords[3].score | 0.6014289855957031 |
| keywords[3].display_name | Degree (music) |
| keywords[4].id | https://openalex.org/keywords/commutative-property |
| keywords[4].score | 0.5679284334182739 |
| keywords[4].display_name | Commutative property |
| keywords[5].id | https://openalex.org/keywords/algebra-over-a-field |
| keywords[5].score | 0.5165099501609802 |
| keywords[5].display_name | Algebra over a field |
| keywords[6].id | https://openalex.org/keywords/differential |
| keywords[6].score | 0.4694882035255432 |
| keywords[6].display_name | Differential (mechanical device) |
| keywords[7].id | https://openalex.org/keywords/pure-mathematics |
| keywords[7].score | 0.4667380750179291 |
| keywords[7].display_name | Pure mathematics |
| keywords[8].id | https://openalex.org/keywords/combinatorics |
| keywords[8].score | 0.24444594979286194 |
| keywords[8].display_name | Combinatorics |
| keywords[9].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[9].score | 0.10000213980674744 |
| keywords[9].display_name | Mathematical analysis |
| keywords[10].id | https://openalex.org/keywords/engineering |
| keywords[10].score | 0.0534881055355072 |
| keywords[10].display_name | Engineering |
| keywords[11].id | https://openalex.org/keywords/physics |
| keywords[11].score | 0.04966050386428833 |
| keywords[11].display_name | Physics |
| language | en |
| locations[0].id | pmh:oai:arXiv.org:2307.08173 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | https://arxiv.org/pdf/2307.08173 |
| locations[0].version | submittedVersion |
| locations[0].raw_type | text |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | |
| locations[0].landing_page_url | http://arxiv.org/abs/2307.08173 |
| locations[1].id | doi:10.48550/arxiv.2307.08173 |
| locations[1].is_oa | True |
| locations[1].source.id | https://openalex.org/S4306400194 |
| locations[1].source.issn | |
| locations[1].source.type | repository |
| locations[1].source.is_oa | True |
| locations[1].source.issn_l | |
| locations[1].source.is_core | False |
| locations[1].source.is_in_doaj | False |
| locations[1].source.display_name | arXiv (Cornell University) |
| locations[1].source.host_organization | https://openalex.org/I205783295 |
| locations[1].source.host_organization_name | Cornell University |
| locations[1].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[1].license | |
| locations[1].pdf_url | |
| locations[1].version | |
| locations[1].raw_type | article |
| locations[1].license_id | |
| locations[1].is_accepted | False |
| locations[1].is_published | |
| locations[1].raw_source_name | |
| locations[1].landing_page_url | https://doi.org/10.48550/arxiv.2307.08173 |
| indexed_in | arxiv, datacite |
| authorships[0].author.id | https://openalex.org/A5064015894 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-4477-8450 |
| authorships[0].author.display_name | Takuro Abe |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Abe, Takuro |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5055862912 |
| authorships[1].author.orcid | |
| authorships[1].author.display_name | Graham Denham |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Denham, Graham |
| authorships[1].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/2307.08173 |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | On Ziegler's conjectures for logarithmic derivations of arrangements |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T06:51:31.235846 |
| primary_topic.id | https://openalex.org/T12812 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9819999933242798 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2604 |
| primary_topic.subfield.display_name | Applied Mathematics |
| primary_topic.display_name | Meromorphic and Entire Functions |
| related_works | https://openalex.org/W2369655046, https://openalex.org/W2019467317, https://openalex.org/W1585519779, https://openalex.org/W1965515989, https://openalex.org/W2088737283, https://openalex.org/W1999587863, https://openalex.org/W1929902734, https://openalex.org/W4376167435, https://openalex.org/W1913119171, https://openalex.org/W2299531140 |
| cited_by_count | 0 |
| locations_count | 2 |
| best_oa_location.id | pmh:oai:arXiv.org:2307.08173 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | https://arxiv.org/pdf/2307.08173 |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | text |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | |
| best_oa_location.landing_page_url | http://arxiv.org/abs/2307.08173 |
| primary_location.id | pmh:oai:arXiv.org:2307.08173 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | https://arxiv.org/pdf/2307.08173 |
| primary_location.version | submittedVersion |
| primary_location.raw_type | text |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | |
| primary_location.landing_page_url | http://arxiv.org/abs/2307.08173 |
| publication_date | 2023-07-16 |
| publication_year | 2023 |
| referenced_works_count | 0 |
| abstract_inverted_index.In | 0, 18 |
| abstract_inverted_index.We | 49, 59 |
| abstract_inverted_index.do | 39 |
| abstract_inverted_index.he | 68 |
| abstract_inverted_index.in | 5, 73 |
| abstract_inverted_index.is | 27 |
| abstract_inverted_index.of | 24, 31 |
| abstract_inverted_index.on | 28 |
| abstract_inverted_index.to | 15, 38, 65 |
| abstract_inverted_index.we | 21 |
| abstract_inverted_index.One | 26 |
| abstract_inverted_index.and | 3, 34, 54 |
| abstract_inverted_index.for | 44 |
| abstract_inverted_index.has | 37 |
| abstract_inverted_index.his | 1 |
| abstract_inverted_index.the | 35, 45, 51, 56 |
| abstract_inverted_index.two | 23 |
| abstract_inverted_index.also | 60 |
| abstract_inverted_index.cuts | 30 |
| abstract_inverted_index.free | 32 |
| abstract_inverted_index.give | 61 |
| abstract_inverted_index.one, | 53 |
| abstract_inverted_index.one. | 58 |
| abstract_inverted_index.some | 62 |
| abstract_inverted_index.this | 19 |
| abstract_inverted_index.with | 40 |
| abstract_inverted_index.1989, | 6 |
| abstract_inverted_index.first | 52 |
| abstract_inverted_index.other | 36 |
| abstract_inverted_index.paper | 2 |
| abstract_inverted_index.posed | 8 |
| abstract_inverted_index.prove | 50 |
| abstract_inverted_index.them. | 25 |
| abstract_inverted_index.using | 70 |
| abstract_inverted_index.degree | 42 |
| abstract_inverted_index.forms. | 48 |
| abstract_inverted_index.posed, | 69 |
| abstract_inverted_index.recent | 71 |
| abstract_inverted_index.second | 57 |
| abstract_inverted_index.thesis | 4 |
| abstract_inverted_index.Ziegler | 7 |
| abstract_inverted_index.algebra | 13 |
| abstract_inverted_index.answers | 64 |
| abstract_inverted_index.generic | 29 |
| abstract_inverted_index.minimal | 41 |
| abstract_inverted_index.related | 14, 66 |
| abstract_inverted_index.revisit | 22 |
| abstract_inverted_index.several | 9 |
| abstract_inverted_index.theory. | 75 |
| abstract_inverted_index.article, | 20 |
| abstract_inverted_index.disprove | 55 |
| abstract_inverted_index.positive | 63 |
| abstract_inverted_index.problems | 67 |
| abstract_inverted_index.regarding | 11 |
| abstract_inverted_index.generators | 43 |
| abstract_inverted_index.hyperplane | 16 |
| abstract_inverted_index.arrangement | 74 |
| abstract_inverted_index.commutative | 12 |
| abstract_inverted_index.conjectures | 10 |
| abstract_inverted_index.logarithmic | 46 |
| abstract_inverted_index.developments | 72 |
| abstract_inverted_index.differential | 47 |
| abstract_inverted_index.arrangements, | 33 |
| abstract_inverted_index.arrangements. | 17 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile |