EQUIVARIANT HOLOMORPHIC EMBEDDINGS FROM THE COMPLEX PROJECTIVE LINE INTO COMPLEX GRASSMANNIAN OF 2-PLANES

Koga, Isami; Nagatomo, Yasuyuki

doi:https://doi.org/10.18910/88483

EQUIVARIANT HOLOMORPHIC EMBEDDINGS FROM THE COMPLEX PROJECTIVE LINE INTO COMPLEX GRASSMANNIAN OF 2-PLANES

Koga, Isami; Nagatomo, Yasuyuki

Osaka Journal of Mathematics, 2022, 59(3), 495-514

アクセス数:325件（2026-07-14 22:28 集計）

固定URL: https://doi.org/10.18910/88483

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タイトル	EQUIVARIANT HOLOMORPHIC EMBEDDINGS FROM THE COMPLEX PROJECTIVE LINE INTO COMPLEX GRASSMANNIAN OF 2-PLANES
著者	NRID 1000060782232 1000060782232 著者名 Koga, Isami
著者	NRID 1000010266075 1000010266075 著者名 Nagatomo, Yasuyuki
抄録	Using gauge theory, we classify SU(2)-equivariant holomorphic embeddings from CP^1 with the Fubini–Study metric into Grassmann manifold Gr_N−2(C^N). It is shown that the moduli spaces of those embeddings are identified with the gauge equivalence classes of non-flat invariant connections satisfying semi-positivity on the vector bundles given by extensions of line bundles. A topology on the moduli is obtained by means of L^2-inner product on Dolbeault cohomology group to which the extension class belongs. The compactification of the moduli is provided with geometric meaning from viewpoint of maps.
出版者	Osaka University and Osaka City University, Departments of Mathematics
収録物名	Osaka Journal of Mathematics
巻(号)	59(3)
ページ	495-514
刊行年月	2022-07
言語	英語
ハンドルURL	https://hdl.handle.net/11094/88483
DOI	https://doi.org/10.18910/88483
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 59, Number 3 （2022-7）

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. 2022, 59(3), p. 495-514
DC.title	EQUIVARIANT HOLOMORPHIC EMBEDDINGS FROM THE COMPLEX PROJECTIVE LINE INTO COMPLEX GRASSMANNIAN OF 2-PLANES
DC.creator	Koga, Isami
DC.creator	Nagatomo, Yasuyuki
DC.publisher	Osaka University and Osaka City University, Departments of Mathematics
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2022-07
DCTERMS.abstract	Using gauge theory, we classify SU(2)-equivariant holomorphic embeddings from CP^1 with the Fubini–Study metric into Grassmann manifold Gr_N−2(C^N). It is shown that the moduli spaces of those embeddings are identified with the gauge equivalence classes of non-flat invariant connections satisfying semi-positivity on the vector bundles given by extensions of line bundles. A topology on the moduli is obtained by means of L^2-inner product on Dolbeault cohomology group to which the extension class belongs. The compactification of the moduli is provided with geometric meaning from viewpoint of maps.
DC.identifier	10.18910/88483
DC.format	88483
citation_title	EQUIVARIANT HOLOMORPHIC EMBEDDINGS FROM THE COMPLEX PROJECTIVE LINE INTO COMPLEX GRASSMANNIAN OF 2-PLANES
citation_author	Koga, Isami
citation_author	Nagatomo, Yasuyuki
citation_publisher	Osaka University and Osaka City University, Departments of Mathematics
citation_language	英語
citation_date	2022-07
citation_journal_title	Osaka Journal of Mathematics
citation_volume	59
citation_issue	3
citation_firstpage	495
citation_lastpage	514
citation_public_url	https://hdl.handle.net/11094/88483
citation_doi_detail	10.18910/88483
citation_doi	https://doi.org/10.18910/88483

EQUIVARIANT HOLOMORPHIC EMBEDDINGS FROM THE COMPLEX PROJECTIVE LINE INTO COMPLEX GRASSMANNIAN OF 2-PLANES

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