Recovery of Vanishing Cycles by Log Geometry : Case of Several Variables

Usui, Sampei; ウスイ, サンペイ; 臼井, 三平

アクセス数:84件（2024-04-18 21:59 集計）

固定URL: https://hdl.handle.net/11094/73420

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タイトル	Recovery of Vanishing Cycles by Log Geometry : Case of Several Variables
著者	NRID 1000090117002 1000090117002 著者名 Usui, Sampei ; ウスイ, サンペイ ; 臼井, 三平
内容	a proceeding of International Conference "Commutative Algebra and Algebraic Geometry and Computational Methods", Hanoi 1996
抄録	This article is a generalization of the author's work [U] to the case of several variables. We first construct compatible actions of monoid S on a “several-variables- version of semi-stable degeneration of pairs” and on the associated log topological spaces introduced by K. Kato and C. Nakayama in [KN]. Here S is the product of the unit interval and the unit circle. Then we show that the associated log topological family is locally piecewise C^∞ trivial over the base, i.e., the associated log topological family recovers the vanishing cycles, in the most naive sense, of the original degeneration. Using this result together with the theory of canonical extensions by Deligne [D], we introduce two types of integral structure of the variation of mixed Hodge structure associated to “several-variables-version of semi-stable degeneration of pairs”. We only sketch the proof here. The complete proof will appear soon somewhere.
出版者	Springer
収録物名	Commutative Algebra, Algebraic Geometry, and Computational Methods
ページ	135-144
刊行年月	1999
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73420
関連情報 (isIdenticalTo)	ISBN 9814021504
関連情報 (isIdenticalTo)	NCID BA42597049
アクセス権	open access
出版タイプ	Accepted Manuscript
カテゴリ	会議発表論文 Conference Paper

資源タイプ	会議発表論文
ローカル資源タイプ	会議発表論文
DCMI資源タイプ	text
DCTERMS.bibliographicCitation	Commutative Algebra, Algebraic Geometry, and Computational Methods. 1999, p. 135-144
DC.title	Recovery of Vanishing Cycles by Log Geometry : Case of Several Variables
DC.creator	Usui, Sampei
	ウスイ, サンペイ
	臼井, 三平
DC.publisher	Springer
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	1999
DC.description	a proceeding of International Conference "Commutative Algebra and Algebraic Geometry and Computational Methods", Hanoi 1996
DCTERMS.abstract	This article is a generalization of the author's work [U] to the case of several variables. We first construct compatible actions of monoid S on a “several-variables- version of semi-stable degeneration of pairs” and on the associated log topological spaces introduced by K. Kato and C. Nakayama in [KN]. Here S is the product of the unit interval and the unit circle. Then we show that the associated log topological family is locally piecewise C^∞ trivial over the base, i.e., the associated log topological family recovers the vanishing cycles, in the most naive sense, of the original degeneration. Using this result together with the theory of canonical extensions by Deligne [D], we introduce two types of integral structure of the variation of mixed Hodge structure associated to “several-variables-version of semi-stable degeneration of pairs”. We only sketch the proof here. The complete proof will appear soon somewhere.
DC.format	application/pdf
citation_title	Recovery of Vanishing Cycles by Log Geometry : Case of Several Variables
citation_author	Usui, Sampei
	ウスイ, サンペイ
	臼井, 三平
citation_publisher	Springer
citation_language	英語
citation_date	1999
citation_journal_title	Commutative Algebra, Algebraic Geometry, and Computational Methods
citation_firstpage	135
citation_lastpage	144
citation_public_url	https://hdl.handle.net/11094/73420

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