| 书目名称 | Iitaka Conjecture |
| 副标题 | An Introduction |
| 编辑 | Osamu Fujino |
| 视频video | |
| 概述 | Is the first introductory textbook for the Iitaka conjecture.Gives a simple new proof of Viehweg‘s conjecture for fiber spaces whose geometric generic fiber is of general type.Provides a very accessib |
| 丛书名称 | SpringerBriefs in Mathematics |
| 图书封面 |  |
| 描述 | 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–M.c.Kernan. 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 f |
| 出版日期 | Book 2020 |
| 关键词 | weakly positive sheaf; semipositivity; big sheaf; Kodaira dimension; logarithmic Kodaira dimension; weak |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-15-3347-1 |
| isbn_softcover | 978-981-15-3346-4 |
| isbn_ebook | 978-981-15-3347-1Series ISSN 2191-8198 Series E-ISSN 2191-8201 |
| issn_series | 2191-8198 |
| copyright | Springer Nature Singapore Pte Ltd. 2020 |
发表于 2025-3-21 19:18:41
