Iitaka Conjecture: An Introduction (SpringerBriefs in Mathematics)

Preface
Acknowledgements
Contents
1 Overview
	1.1 What is the Iitaka Program?
	1.2 The Main Results
	1.3 Historical Note
	1.4 Precise Contents
	1.5 References
2 Preliminaries
	2.1 Notations, Terminology, and Conventions
	2.2 Prerequisites
	2.3 Preliminary Results
		2.3.1 Basic Definitions
		2.3.2 Iitaka Dimension and Kodaira Dimension
		2.3.3 Cyclic Covers
		2.3.4 Weakly Semistable Morphisms
		2.3.5 Kollár's Torsion-Freeness and Vanishing Theorem
		2.3.6 On Abelian Varieties
		2.3.7 Invariance of Plurigenera
		2.3.8 Related Conjectures
3 Viehweg's Weak Positivity
	3.1 Weakly Positive Sheaves and Big Sheaves
	3.2 Effective Freeness Due to Popa–Schnell
	3.3 Direct Images of Relative Pluricanonical Bundles
	3.4 Some Further Developments
		3.4.1 Singular Hermitian Metrics on Torsion-Free Coherent Sheaves by Păun–Takayama
		3.4.2 Nakayama's Theory of ω-Sheaves, and so on
		3.4.3 Twisted Weak Positivity and Effective Generation By Dutta–Murayama
4 Iitaka–Viehweg Conjecture for Some Special Cases
	4.1 From Viehweg's Conjecture to Iitaka's Conjecture
	4.2 Fiber Spaces Whose Base Space is of General Type
	4.3 Fiber Spaces Whose Geometric Generic Fiber is of General Type
	4.4 Elliptic Fibrations
	4.5 Some Other Cases
		4.5.1 Fiber Spaces Whose Base Space Has Maximal Albanese Dimension
		4.5.2 Fiber Spaces Whose Geometric Generic Fiber Has a Good Minimal Model
		4.5.3 Iitaka Conjecture in Positive Characteristic
5 overlineCn, n-1 Revisited
	5.1 Background of overlineCn, n-1
	5.2 overlineCn, n-1
	5.3 Some Related Results
		5.3.1 Conjecture overlineCn, m for Affine Varieties, and so on
		5.3.2 Subadditivity Due to Kovács–Patakfalvi and Hashizume
	5.4 Appendix: A Vanishing Lemma
6 Appendices
	6.1 C2,1
	6.2 Conjectures ()n and (>)n
Appendix  References
Index