LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES

Daigle, Daniel; Melle-Hernándes, Alejandro

doi:info:doi/10.18910/29206

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タイトル	LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES
著者	Daigle, Daniel Daigle, Daniel
著者	Melle-Hernándes, Alejandro Melle-Hernándes, Alejandro
抄録	Given a unicuspidal rational curve C ⊂ P^2 with singular point P, we study the unique pencil Λ_C on P^2 satisfying C ∈ Λ_C and B_s(Λ_C) = {P}. We show that the general member of Λ_C is a rational curve if and only if ν^^~(C) ≥ 0, where ν^^~(C) denotes the self-intersection number of C after the minimal resolution of singularities. We also show that if ν^^~(C) ≥ 0, then Λ_C has a dicritical of degree 1. Note that all currently known unicuspidal rational curves C ⊂ P^2 satisfy ν^^~(C) ≥ 0.
公開者	Osaka University and Osaka City University, Departments of Mathematics
掲載誌名	Osaka Journal of Mathematics
巻	51
号	2
開始ページ	481
終了ページ	511
刊行年月	2014-04
ISSN	00306126
NCID	AA00765910
URL	http://hdl.handle.net/11094/29206
言語	英語
DOI	info:doi/10.18910/29206
カテゴリ	紀要論文 Departmental Bulletin Paper
カテゴリ	Osaka Journal of Mathematics / Volume 51, Number 2　(2014-4）

著者版フラグ	publisher
NII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.51(2) P.481-P.511
DC.title	LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES
DC.creator	Daigle, Daniel
DC.creator	Melle-Hernándes, Alejandro
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language" scheme="DCTERMS.RFC1766	英語
DCTERMS.issued" scheme="DCTERMS.W3CDTF	2014-04
DC.identifier" scheme="DCTERMS.URI	http://hdl.handle.net/11094/29206
DCTERMS.abstract	Given a unicuspidal rational curve C ⊂ P^2 with singular point P, we study the unique pencil Λ_C on P^2 satisfying C ∈ Λ_C and B_s(Λ_C) = {P}. We show that the general member of Λ_C is a rational curve if and only if ν^^~(C) ≥ 0, where ν^^~(C) denotes the self-intersection number of C after the minimal resolution of singularities. We also show that if ν^^~(C) ≥ 0, then Λ_C has a dicritical of degree 1. Note that all currently known unicuspidal rational curves C ⊂ P^2 satisfy ν^^~(C) ≥ 0.
DC.identifier	info:doi/10.18910/29206
citation_title	LINEAR SYSTEMS ASSOCIATED TO UNICUSPIDAL RATIONAL PLANE CURVES
citation_author	Daigle, Daniel
citation_author	Melle-Hernándes, Alejandro
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2014-04
citation_journal_title	Osaka Journal of Mathematics
citation_volume	51
citation_issue	2
citation_firstpage	481
citation_lastpage	511
citation_issn	00306126
citation_public_url	http://hdl.handle.net/11094/29206
citation_doi	info:doi/10.18910/29206

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