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Iitaka Conjecture : an introduction / Osamu Fujino.

Wed, 11 Nov 2020 18:15:36 +0900

Osamu Fujino.. Iitaka Conjecture : an introduction. Springer, [2020], SpringerBriefs in Mathematics. ISBN:9789811533464; 9811533466; 9789811533471; 9811533474
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.

Foundations of the minimal model program / author Osamu Fujino

Fri, 14 Jul 2017 23:14:56 +0900

author Osamu Fujino. Foundations of the minimal model program. The Mathematical Society of Japan, 2017, MSJ memoirs ; volume 35. ISBN:978-4-86497-045-7

Minimal models and extremal rays (Kyoto, 2011) / edited by János Kollár, Osamu Fujino, Shigeru Mukai, Noboru Nakayama

Thu, 27 Oct 2016 00:49:26 +0900

edited by János Kollár, Osamu Fujino, Shigeru Mukai, Noboru Nakayama. Minimal models and extremal rays (Kyoto, 2011). The Mathematical Society of Japan, c2016, Advanced studies in pure mathematics ; 70. ISBN:978-4-86497-036-5

Development of moduli theory-Kyoto 2013 / edited by Osamu Fujino, Shigeyuki Kondō, Atsushi Moriwaki, Masa-hiko Saito, Kōta Yoshioka

Thu, 29 Sep 2016 19:52:07 +0900

edited by Osamu Fujino, Shigeyuki Kondō, Atsushi Moriwaki, Masa-hiko Saito, Kōta Yoshioka. Development of moduli theory-Kyoto 2013. The Mathematical Society of Japan, c2016, Advanced studies in pure mathematics ; 69. ISBN:978-4-86497-032-7