ARRANGEMENTS, HOMOLOGY PLANES AND FUNDAMENTAL GROUPS

Aguilar Aguilar, Rodolfo

doi:https://doi.org/10.18910/101128

ARRANGEMENTS, HOMOLOGY PLANES AND FUNDAMENTAL GROUPS

Aguilar Aguilar, Rodolfo

Osaka Journal of Mathematics, 2025, 62(2), 233-279

アクセス数:51件（2026-02-16 10:17 集計）

固定URL: https://doi.org/10.18910/101128

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タイトル	ARRANGEMENTS, HOMOLOGY PLANES AND FUNDAMENTAL GROUPS
著者	著者名 Aguilar Aguilar, Rodolfo
抄録	Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in particular, to homology planes arising from arrangements of lines. In certain cases, the presentation is trivial, and we can obtain infinite new exotic algebraic and analytic structures on ℂⁿ for n ≥ 3. We also find the first examples of homology planes of log-general type with an infinite fundamental group. The infiniteness can be obtained geometrically by orbifold morphisms to orbicurves.
出版者	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
収録物名	Osaka Journal of Mathematics
巻(号)	62(2)
ページ	233-279
刊行年月	2025-04
言語	英語
ハンドルURL	https://hdl.handle.net/11094/101128
DOI	https://doi.org/10.18910/101128
PISSN	00306126
NCID	AA00765910
アクセス権	open access
出版タイプ	Version of Record
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 62, Number 2 （2025-04）

資源タイプ	紀要論文
ローカル資源タイプ	紀要論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Osaka Journal of Mathematics. 2025, 62(2), p. 233-279
DC.title	ARRANGEMENTS, HOMOLOGY PLANES AND FUNDAMENTAL GROUPS
DC.creator	Aguilar Aguilar, Rodolfo
DC.publisher	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2025-04
DCTERMS.abstract	Following our previous work, we develop an algorithm to compute a presentation of the fundamental group of certain partial compactifications of the complement of a complex arrangement of lines in the projective plane. It applies, in particular, to homology planes arising from arrangements of lines. In certain cases, the presentation is trivial, and we can obtain infinite new exotic algebraic and analytic structures on ℂⁿ for n ≥ 3. We also find the first examples of homology planes of log-general type with an infinite fundamental group. The infiniteness can be obtained geometrically by orbifold morphisms to orbicurves.
DC.identifier	10.18910/101128
DC.format	101128
citation_title	ARRANGEMENTS, HOMOLOGY PLANES AND FUNDAMENTAL GROUPS
citation_author	Aguilar Aguilar, Rodolfo
citation_publisher	Departments of Mathematics, The University of Osaka and Osaka Metropolitan University
citation_language	英語
citation_date	2025-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	62
citation_issue	2
citation_firstpage	233
citation_lastpage	279
citation_public_url	https://hdl.handle.net/11094/101128
citation_doi_detail	10.18910/101128
citation_doi	https://doi.org/10.18910/101128

ARRANGEMENTS, HOMOLOGY PLANES AND FUNDAMENTAL GROUPS

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