Scientists / Open questions
Shigefumi Mori
Algebraic geometry; birational geometry
1990 Fields Medal
5 questions
Preservation of divisorial contraction type under deformation of extremal rays: the exceptional (3.3.3)/(3.3.4) swap in Mori's lifting theorem for smooth families of threefolds
Does negative Kodaira dimension imply uniruledness? The open Nonvanishing core of the uniruledness–Kodaira-dimension conjecture
Termination of flips in dimension at least 5 and non-vanishing for minimal models in dimension at least 4: the open core of the higher-dimensional minimal model program raised in Mori's flip theorem paper (1988)
Complete the classification of three-dimensional extremal curve germs with reducible central curve: the semistable case 12o, Reid's general elephant conjecture there, sharp bounds on the number of components, and the existence of case 10o
Multiple fibers of del Pezzo fibrations: the unrealized types and , the cyclic-quotient conjecture for multiplicity at least 5, and the local structure along a multiple fiber