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Iitaka conjecturean introduction /

Fujino, Osamu.

Iitaka conjecturean introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Iitaka conjectureby Osamu Fujino.
Reminder of title:	an introduction /
Author:	Fujino, Osamu.
Published:	Singapore :Springer Singapore :2020.
Description:	xiv, 128 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Algebraic varieties.
Online resource:	https://doi.org/10.1007/978-981-15-3347-1
ISBN:	9789811533471$q(electronic bk.)

Iitaka conjecturean introduction /
Fujino, Osamu.

Iitaka conjecturean introduction /[electronic resource] :by Osamu Fujino. - Singapore :Springer Singapore :2020. - xiv, 128 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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.

ISBN: 9789811533471$q(electronic bk.)

Standard No.: 10.1007/978-981-15-3347-1doiSubjects--Topical Terms:

387264
Algebraic varieties.

LC Class. No.: QA564 / .F855 2020

Dewey Class. No.: 516.353

Iitaka conjecturean introduction /
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520 $a 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.
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