Theory of mixed log Hodge structures and its applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 23340008
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Osaka University
• Principal Investigator: USUI Sampei 大阪大学, その他部局等, 名誉教授 (90117002)
• Co-Investigator(Kenkyū-buntansha): NAKAYAMA Chikara 一橋大学, 大学院経済学研究科, 教授 (70272664) ; KONNO Kazuhiro 大阪大学, 大学院理学研究科, 教授 (10186869) ; ASHIKAGA Tadashi 東北学院大学, 工学部, 教授 (90125203) ; FUJIKI Akira 大阪大学, その他部局等, 名誉教授 (80027383) ; OGUISO Keiji 東京大学, 大学院数理科学研究科, 教授 (40224133) ; TAKAHASHI Atsushi 大阪大学, 大学院理学研究科, 教授 (50314290) ; OHNO Koji 大阪大学, 大学院理学研究科, 助教 (20252570) ; WATANABE Kenta 大阪大学, 理学(系)研究科(研究院), 研究員 (70582683)
• Co-Investigator(Renkei-kenkyūsha): KATO Kazuya シカゴ大学, 教授 (90111450)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: ホッジ理論 / 周期写像 / モジュライ / コンパクト化 / 混合対数的ホッジ構造 / 混合版基本図式 / ネロンモデル / ミラー対称性

Outline of Final Research Achievements

In mixed case, we constructed spaces of SL(2)-orbits, fine moduli of log mixed Hodge structures. As geometric applications, we constructed Neron models and showed analyticity of the common zeros of sections of the Neron model. We also constructed a Neron model which accepts any given admissible normal function. As applications of these results to physics, we describe closed and open mirror symmetry for quantic 3-folds. All of these results are published.
In mixed case, supplementing spaces of nilpotent i-orbits with ratio structure and spaces of SL(2)-orbit with star, we completed an amplified fundamental diagram by which various limits of period maps and normal functions are compared. These results are submitted and available from arXiv.

Free Research Field

数理系科学