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Beschreibung
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 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. 80,24 €
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Technische Daten
Erscheinungsdatum
10.04.2020
Sprache
Englisch
EAN
9789811533464
Herausgeber
Springer Singapore
Serien- oder Bandtitel
SpringerBriefs in Mathematics
Sonderedition
Nein
Autor
Osamu Fujino
Seitenanzahl
128
Einbandart
Broschiert
Buch Untertitel
An Introduction
Schlagwörter
weakly positive sheaf, semipositivity, big sheaf, Kodaira dimension, logarithmic Kodaira dimension, weak semistable reduction, Iitaka conjecture, generalized Iitaka conjecture, Viehweg conjecture, effective freeness
Thema-Inhalt
PBMW - Algebraische Geometrie
PBKD - Komplexe Analysis, komplexe Variablen, Funktionentheorie
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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