國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Iitaka conjecturean introduction /

Fujino, Osamu.

Iitaka conjecturean introduction /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Iitaka conjectureby Osamu Fujino.
其他題名:	an introduction /
作者:	Fujino, Osamu.
出版者:	Singapore :Springer Singapore :2020.
面頁冊數:	xiv, 128 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Algebraic varieties.
電子資源:	https://doi.org/10.1007/978-981-15-3347-1
ISBN:	9789811533471$q(electronic bk.)

Iitaka conjecturean introduction /
Fujino, Osamu.

Iitaka conjecturean introduction /[electronic resource] :by Osamu Fujino. - Singapore :Springer Singapore :2020. - xiv, 128 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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 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.

ISBN: 9789811533471$q(electronic bk.)

Standard No.: 10.1007/978-981-15-3347-1doiSubjects--Topical Terms:

387264
Algebraic varieties.

LC Class. No.: QA564 / .F855 2020

Dewey Class. No.: 516.353

Iitaka conjecturean introduction /
LDR:02695nmm a2200337 a 4500 001 572079
003 DE-He213
005 20200818095940.0
006 m d
007 cr nn 008maaau
008 200922s2020 si s 0 eng d
020 $a 9789811533471$q(electronic bk.)
020 $a 9789811533464$q(paper)
024 7 $a 10.1007/978-981-15-3347-1 $2 doi
035 $a 978-981-15-3347-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA564 $b .F855 2020
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.353 $2 23
090 $a QA564 $b .F961 2020
100 1 $a Fujino, Osamu. $3 858973
245 1 0 $a Iitaka conjecture $h [electronic resource] : $b an introduction / $c by Osamu Fujino.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a xiv, 128 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a Overview -- Preliminaries -- Viehweg's Weak Positivity -- Iitaka-Viehweg conjecture for Some Special Cases -- Cn,n-1 Revisited -- Appendices.
520 $a 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.
650 0 $a Algebraic varieties. $3 387264
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 276692
650 2 4 $a Commutative Rings and Algebras. $3 274057
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 558795
856 4 0 $u https://doi.org/10.1007/978-981-15-3347-1
950 $a Mathematics and Statistics (Springer-11649)