LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Iitaka Conjecture ([EBook]) : An Introduction / by Osamu Fujino.
Author	Fujino, Osamu
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2020.
Publication	Singapore : Springer Singapore , 2020.
Physical Details	XIV, 128 pages: 1 illus. : online resource.
Series	SpringerBriefs in Mathematics 2191-8198
ISBN	9789811533471
Summary Note	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.:
Contents note	Overview -- Preliminaries -- Viehweg's Weak Positivity -- Iitaka-Viehweg conjecture for Some Special Cases -- Cn,n-1 Revisited -- Appendices.
Mode of acces to digital resource	Digital book. Cham Springer Nature 2020. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher). Available as searchable text in PDF format
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-981-15-3347-1
Links to Related Works	Subject References: Algebraic Geometry . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Functions of complex variables . Several Complex Variables and Analytic Spaces . Authors: author . Fujino, Osamu . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 516.35 . 516.35 (DDC 23) .

Catalogue Display

Iitaka Conjecture: An Introduction

Reviews