Complex geometry of relative pluricanonical bundles and deformation spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 23340013
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Tokyo
• Principal Investigator: Takayama Shigeharu 東京大学, 数理(科)学研究科(研究院), 教授 (20284333)
• Co-Investigator(Renkei-kenkyūsha): FUTAKI Akito 東京大学, 大学院数理科学研究科, 教授 (90143247) ; GOTO Ryushi 大阪大学, 大学院理学研究科, 教授 (30252571) ; OHSAWA Takeo 名古屋大学, 大学院多元数理科学研究科, 教授 (30115802) ; OBITSU Kunio 鹿児島大学, 大学院理工学研究科, 准教授 (00325763) ; YAMANOI Katsutoshi 大阪大学, 大学院理学研究科, 教授 (40335295) ; FUJINO Osamu 京都大学, 大学院理学研究科, 准教授 (60324711) ; HAYASHIMOTO Atsushi 国立長野高専, 一般科, 准教授 (90342493)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 相対標準束 / モジュライ空間 / 変形空間

Outline of Final Research Achievements

For a proper surjective morphism between complex manifolds, we obtain results to connect the deformation of complex structures of fibers and the curvature property or variations of the relative pluricanonical bundle and its direct image equipped with canonically attached Hermitian metrics. In particular, when the fibers are Calabi-Yau type, we describe completely the relations among the behavior of fiberwise Kahler-Einstein metrics, the completeness of the Weil-Petersson metric on the base, and the possible type of singularities on the central fiber.

Free Research Field

複素幾何学