A study of mirror symmetry through log mixed Hodge theory

Usui, Sampei

A study of mirror symmetry through log mixed Hodge theory

Usui, Sampei

Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics Hodge Theory, Complex Geometry, and Representation Theory, Texas Christian University, Fort Worth, Texas, June 18, 2012, 2014, 285-311

アクセス数:173件（2025-03-22 22:10 集計）

固定URL: https://hdl.handle.net/11094/73429

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タイトル	A study of mirror symmetry through log mixed Hodge theory
著者	NRID 1000090117002 1000090117002 著者名 Usui, Sampei ; ウスイ, サンペイ ; 臼井, 三平
内容	First published in Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics Hodge Theory, Complex Geometry, and Representation Theory, Texas Christian University, Fort Worth, Texas, June 18, 2012, published by American Mathematical Society
内容	Contemporary mathematics, 608
抄録	We hope to understand the Hodge theoretic aspect of mirror symmetry in the framework of the fundamental diagram of log mixed Hodge theory. This paper is a first step. We give a formulation of the mirror theorem for quintic threefolds and their mirror as the coincidence of log period maps with specified sections under the mirror map. Since a variation of Hodge structure with unipotent monodromy on a punctured disc uniquely extends over the puncture to a log Hodge structure, we can work on and over the boundary point, and we can observe clearly in high-resolution the behavior of the Z-structure over the boundary point. This is an advantage of log Hodge theory.
出版者	American Mathematical Society
収録物名	Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics Hodge Theory, Complex Geometry, and Representation Theory, Texas Christian University, Fort Worth, Texas, June 18, 2012
ページ	285-311
刊行年月	2014
言語	英語
ハンドルURL	https://hdl.handle.net/11094/73429
関連情報 (isIdenticalTo)	ISBN 9780821894156
関連情報 (isIdenticalTo)	NCID BB14936303
アクセス権	open access
権利情報	© 2014 by the American Mathematical Society. All rights reserved.
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	Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics Hodge Theory, Complex Geometry, and Representation Theory, Texas Christian University, Fort Worth, Texas, June 18, 2012. 2014, p. 285-311
DC.title	A study of mirror symmetry through log mixed Hodge theory
DC.creator	Usui, Sampei
	ウスイ, サンペイ
	臼井, 三平
DC.publisher	American Mathematical Society
DC.language' scheme='DCTERMS.RFC1766	英語
DC.type' scheme='DCTERMS.DCMIType	text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2014
DC.description	First published in Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics Hodge Theory, Complex Geometry, and Representation Theory, Texas Christian University, Fort Worth, Texas, June 18, 2012, published by American Mathematical Society
DC.description	Contemporary mathematics, 608
DCTERMS.abstract	We hope to understand the Hodge theoretic aspect of mirror symmetry in the framework of the fundamental diagram of log mixed Hodge theory. This paper is a first step. We give a formulation of the mirror theorem for quintic threefolds and their mirror as the coincidence of log period maps with specified sections under the mirror map. Since a variation of Hodge structure with unipotent monodromy on a punctured disc uniquely extends over the puncture to a log Hodge structure, we can work on and over the boundary point, and we can observe clearly in high-resolution the behavior of the Z-structure over the boundary point. This is an advantage of log Hodge theory.
DC.rights	© 2014 by the American Mathematical Society. All rights reserved.
DC.format	73429
citation_title	A study of mirror symmetry through log mixed Hodge theory
citation_author	Usui, Sampei
citation_publisher	American Mathematical Society
citation_language	英語
citation_date	2014
citation_journal_title	Hodge theory, complex geometry, and representation theory : NSF-CBMS Regional Conference in Mathematics Hodge Theory, Complex Geometry, and Representation Theory, Texas Christian University, Fort Worth, Texas, June 18, 2012
citation_firstpage	285
citation_lastpage	311
citation_public_url	https://hdl.handle.net/11094/73429

A study of mirror symmetry through log mixed Hodge theory

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