6 papers
Partial desingularization up to normal-crossings in characteristic 0 and 2
Dan Abramovich, Michael Temkin
We address the question of normal-crossings-preserving resolution of singularities (NC-preserving resolution), and compare the cases of characteristic 0 and characteristic 2. In ch…
Torus actions, weighted blow-ups, and desingularization of plane curves
Dan Abramovich, Ming Hao Quek, Bernd Schober
Given a singular hypersurface in a regular 2-dimensional scheme essentially of finite type over a field, we construct an embedded resolution of singularities by weighted blow-ups.…
Principalization on logarithmically foliated orbifolds
Dan Abramovich, André Belotto da Silva, Michael Temkin +1
In characteristic zero, we construct principalization of ideals on smooth orbifolds endowed with a normal crossings divisor and a foliation. We then illustrate how the method can b…
Functorial monomialization and uniqueness of centers for relative principalization
Dan Abramovich, Michael Temkin, JarosÅaw WÅodarczyk
Theorem 1.2.6 of [ATW20] provides a relatively functorial logarithmic principalization of ideals on relative logarithmic orbifolds in characteristic 0, relying on a delica…
Logarithmic resolution of singularities in characteristic 0 using weighted blow-ups
Dan Abramovich, André belotto da Silva, Ming Hao Quek +2
In characteristic zero, we construct logarithmic resolution of singularities, with simple normal crossings exceptional divisor, using weighted blow-ups.
Resolving plane curves using stack-theoretic blow-ups
Dan Abramovich, Ming Hao Quek, Bernd Schober
Stack-theoretic blow-ups have proven to be efficient in resolving singularities over fields of characteristic zero. In this article, we move forward towards positive characteristic…