Toward the second main theorem on complements: from local to global
arXiv:math/0606242
Abstract
We prove the boundedness of complements modulo two conjectures: Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.
46 pages, LaTeX, third version, we made some changes to improve presentation, to appear in Journal of Algebraic Geometry