Iitaka Conjecture

“This book is the first monograph about the Iitaka conjecture, a central conjecture in complex algebraic geometry. This survey is intended for graduate students and researchers who want to obtain a panoramic view of this profound conjecture. … This very nice textbook covers in a pedagogical way the key results about positivity of direct image sheaves and gives a much better understanding of the Iitaka conjecture from the perspective of the minimal model program.” (Julien Keller, Mathematical Reviews, April, 2022)“The importance of Iitaka’s conjecture is obvious to anyone who is aware of the notion of Kodaira dimension and its rôle in classification theory. … the literature on positivity of direct image sheaves is vast and highly technical, this text gathers the most fundamental tools and makes Viehweg’s theory more accessible. The use of the more recent contributions to the minimal model program simplifies some arguments, exposed in the author’s precise style of writing.” (Andreas Höring, zbMATH 1452.14002, 2021)

• Overview.- Preliminaries.- Viehweg’s Weak Positivity.- Iitaka–Viehweg conjecture for Some Special Cases.- Cn,n-1 Revisited.- Appendices.