Resolution of singularities

For the technique used for graph C*-algebras and Leavitt path algebras, see Graph C*-algebra § Desingularization.
Strong desingularization of Observe that the resolution does not stop after the first blowing-up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors.

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0, this was proved by Heisuke Hironaka in 1964;[1] while for varieties of dimension at least 4 over fields of characteristic p, it is an open problem.[2]

  1. ^ Hironaka 1964.
  2. ^ Hauser 2010.