185 citations · 736 across the 61 of their papers we have counts for
64 papers
Resolution of singularities for the dynamical mathematician
Dan Abramovich
I begin by explaining to non-specialists why resolution of singularities in characteristic 0 works. Then I go into some ideas telling how it actually works. I finish with a brief d…
The integral Chow ring of weighted blow-ups
Veronica Arena, Stephen Obinna, Dan Abramovich
We give a formula for the integral Chow rings of weighted blow-ups. Along the way, we also compute the integral Chow rings of weighted projective stack bundles, a formula for the G…
Desingularization of binomial varieties using toric Artin stacks
Dan Abramovich, Bernd Schober
We show how the notion of fantastacks can be used to effectively desingularize binomial varieties defined over algebraically closed fields. In contrast to a desingularization via b…
Logarithmic resolution via multi-weighted blow-ups
Dan Abramovich, Ming Hao Quek
We first introduce and study the notion of multi-weighted blow-ups, which is later used to systematically construct an explicit yet efficient algorithm for functorial logarithmic r…
Punctured logarithmic maps
Dan Abramovich, Qile Chen, Mark Gross +1
We introduce a variant of stable logarithmic maps, which we call punctured logarithmic maps. They allow an extension of logarithmic Gromov-Witten theory in which marked points have…
Relative desingularization and principalization of ideals
Dan Abramovich, Michael Temkin, Jarosław Włodarczyk
In characteristic zero, we construct relative principalization of ideals for logarithmically regular morphisms of logarithmic schemes, and use it to construct logarithmically regul…