Iitaka Conjecture : An Introduction. 1st ed. 2020

種類:

電子ブック

責任表示:

by Osamu Fujino

出版情報:

Singapore : Springer Nature Singapore : Imprint: Springer, 2020

著者名:

• Fujino, Osamu.
• SpringerLink (Online service)

シリーズ名:

SpringerBriefs in Mathematics ;

ISBN:

9789811533471 [9811533474]    

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 Ii

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