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Viser: Iitaka Conjecture - An Introduction
Iitaka Conjecture Vital Source e-bog
Osamu Fujino
(2020)
Iitaka Conjecture
An Introduction
Osamu Fujino
(2020)
Sprog: Engelsk
Detaljer om varen
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Springer Nature (April 2020)
- ISBN: 9789811533471
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Detaljer om varen
- Paperback
- Udgiver: Springer (April 2020)
- ISBN: 9789811533464
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.