Scientists / Open questions
Heisuke Hironaka
Algebraic geometry; resolution of singularities
1970 Fields Medal
3 questions
Smoothability of algebraic cycles below the middle dimension in positive characteristic: the surviving core of Hironaka's smoothing problem
Stabilization of iterated Nash blow-ups along non-divisorial valuations: extending Hironaka's divisorial stabilization theorem
Resolution of singularities in positive and mixed characteristic, dimension at least four: the open core left by Hironaka's 1964 characteristic-zero theorem