4 papers · 1 filter
Elimination with applications to singularities in positive characteristic
Orlando Villamayor
We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a functi…
Rees algebras and resolution of singularities
Santiago Encinas, Orlando Villamayor
Embedded principalization of ideals in smooth schemes, also known as Log-resolutions of ideals, play a central role in algebraic geometry. If two sheaves of ideals, say and $…
A Proof of Desingularization over fields of characteristic zero
S. Encinas, O. Villamayor
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness. This proo…
On Algorithmic Equiresolution and Stratification of Hilbert Schemes
S. Encinas, A. Nobile, O. Villamayor
Given an algorithm of resolution of singularities satisfying certain conditions (``good algorithms''), natural notions of simultaneous algorithmic resolution, or equiresolution, fo…