Project/Area Number  09640129 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

Research Institution  Sophia University 
Principal Investigator 
KATO Masahide Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (90062679)

CoInvestigator(Kenkyūbuntansha) 
TAHARA Hidetoshi Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (60101028)
KANEYUKI Soji Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (40022553)
NAGANO Tadashi Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (10189144)
YOKOYAMA Kazuo Sophia University, Department of Mathematics, Asso. Professor, 理工学部, 助教授 (10053711)
MIYAOKA Reiko Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (70108182)
谷口 肇 上智大学, 理工学部, 助教授 (40053657)
並河 良典 上智大学, 理工学部, 助教授 (80228080)

Project Period (FY) 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥3,400,000 (Direct Cost : ¥3,400,000)
Fiscal Year 1999 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  complex manifold / projective structure / Gauduchon metric / Hartogs domain / nonKahler / extension peoblem / Weyl curvature teusor / Chern forms / Characteristic forms / projective connections / 正則写像 / Gauduchonメトリック / 特異ファイバー / 正則拡張性 
Research Abstract 
Our main object of study is a class of compact complex 3manifolds which contain a subdomain U biholomorphic to a neighborhood of a projective line ill a complex projective 3space. We call such a class of manifolds by Class L. Such manifolds do not admit projective structures in general, but very deeply related to complex manifolds which admit projective structures. To classify all Class L. manifolds, it seems very important to consider the existence problem of Cauduchon metric near a singular fibre of a 1parameter family of surfaces, and we are now very near to the complete solution. To carry out our plan of classification of Class L manifolds, a series of theorems of S. Ivashkovich on the extension of meromorphic maps play important roles. On the other hand, our manifolds of Class L supply us with many interesting examples on extension problems of meromorphic maps. N. Okada (Sophia Univ. Graduate Course) constructed an example of Schottky type Class L manifolds, gave a holomorphic map of a Hartogs domain to the manifold whichl cannot he extended meromorphically across a fractal set, and estimated the Hausdorff dimension of the singular set. With Y. Kamozawa (NTT), we have obtained a explicit formula of characteristic forms on a holomorphic foliation which admits a holomorphic projective connection.
