Abstract Generalised pairs are a natural structure in birational geometry that first appeared in Kodaira’s canonical bundle formula for elliptic fibrations. They were formally introduced by Birkar and Zhang in 2014 as part of their study of effective Iitaka fibrations and have since become a central topic in modern-day birational geometry. In particular, they have been essential in Birkar proo...
AbstractThere are two main obstacles in extending the Minimal Model Program (MMP) for Kahler varieties: (i) given a compact Kahler manifold X, if the canonical bundle K_X is not nef, then does there exist a rational curve C\subset of X such that K_X\cdot C