Constructive General Neron Desingularization for one dimensional local rings

Construction of Neron Desingularization for Two Dimensional Rings

An algorithmic proof of the General Neron Desingularization theorem is given for 2dimensional local rings and morphisms with small singular locus.

Inseparable Local Uniformization

The aim of this paper is to prove that an algebraic variety over a field can be desingularized locally along a valuation after a purely inseparable alteration. Zariski was first to study the problem of desingularizing algebraic varieties along valuations. He called this problem local uniformization of valuations and observed that it should be considered as the local part of the desingularizatio...

An Introduction to Constructive Desingularization.

Genus-one Stable Maps, Local Equations, and Vakil-zinger’s Desingularization

We describe an algebro-geometric approach to Vakil-Zinger’s desingularization of the main component of the moduli of genus one stable maps to P [6, 7]. The new approach provides complete local structural results for this moduli space as well as for the desingularization of the entire moduli space and should fully extend to higher genera.

Strengthening the Theorem of Embedded Desingularization

Resolution of singularities is one of the central areas of research in Algebraic Geometry. It is a basic prerequisite for the classification of algebraic varieties up to birational equivalence, since it allows to consider only regular varieties. Hironaka’s monumental work [Hi1] gave a non-constructive, existence proof of resolution of singularities over fields of characteristic zero. Constructi...