---

＜電子ブック＞
Iitaka Conjecture : An Introduction / by Osamu Fujino
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2020.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2020
大きさ	XIV, 128 p. 1 illus : online resource
著者標目	*Fujino, Osamu author SpringerLink (Online service)
件　名	LCSH:Algebraic geometry LCSH:Functions of complex variables LCSH:Commutative algebra LCSH:Commutative rings FREE:Algebraic Geometry FREE:Several Complex Variables and Analytic Spaces FREE:Commutative Rings and Algebras
一般注記	Overview -- Preliminaries -- Viehweg’s Weak Positivity -- Iitaka–Viehweg conjecture for Some Special Cases -- Cn,n-1 Revisited -- Appendices The ambitious program for the birational classification of higher-dimensional complex algebraic varieties initiated by Shigeru Iitaka around 1970 is usually called the Iitaka program. Now it is known that the heart of the Iitaka program is the Iitaka conjecture, which claims the subadditivity of the Kodaira dimension for fiber spaces. The main purpose of this book is to make the Iitaka conjecture more accessible. First, Viehweg's theory of weakly positive sheaves and big sheaves is described, and it is shown that the Iitaka conjecture follows from the Viehweg conjecture. Then, the Iitaka conjecture is proved in some special and interesting cases. A relatively simple new proof of Viehweg's conjecture is given for fiber spaces whose geometric generic fiber is of general type based on the weak semistable reduction theorem due to Abramovick–Karu and the existence theorem of relative canonical models by Birkar–Cascini–Hacon–McKernan. No deep results of the theory of variations of Hodge structure are needed. The Iitaka conjecture for fiber spaces whose base space is of general type is also proved as an easy application of Viehweg's weak positivity theorem, and the Viehweg conjecture for fiber spaces whose general fibers are elliptic curves is explained. Finally, the subadditivity of the logarithmic Kodaira dimension for morphisms of relative dimension one is proved. In this book, for the reader's convenience, known arguments as well as some results are simplified and generalized with the aid of relatively new techniques HTTP:URL=https://doi.org/10.1007/978-981-15-3347-1

 類似資料