8 papers
Non-normalized Nash blowup fails to resolve singularities in dimension three
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez +1
In this paper we show that iterating (non-normalized) Nash blowups does not necessarily resolve the singularities of algebraic varieties of dimension three over fields of character…
On a Computational Approach to the Nash Blowup Problem
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez +1
In this paper we describe the implementation that led to the counterexamples to the Nash blowup conjectures recently discovered by the authors. We also provide new examples of tori…
The Euler characteristic of Milnor fibers over 2-generic symmetric determinantal varieties
Thaís M. Dalbelo, Daniel Duarte, Danilo da Nóbrega Santos
In this work we present a formula for the Euler characteristic of the Milnor fiber of non-degenerate functions with isolated critical set relative to a strati…
Characteristic-free normalized Nash blowup of toric varieties
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez +1
We introduce conditions on cones of normal toric varieties under which the polyhedron defining the normalized Nash blowup does not depend on the characteristic of the base field. A…
Nash blowups of normal toric surfaces: the case of one and two segments
Daniel Duarte, Jawad Snoussi
We show that iterating Nash blowups resolve the singularities of normal toric surfaces satisfying the following property: the minimal generating set of the corresponding semigroup…
Nash blowup fails to resolve singularities in dimensions four and higher
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez +1
In this paper we show that iterating Nash blowups or normalized Nash blowups does not resolve the singularities of algebraic varieties of dimension four or higher over an algebraic…
Nash blowups of 2-generic determinantal varieties in positive characteristic
Thaís M. Dalbelo, Daniel Duarte, Maria Aparecida Soares Ruas
We show that the Nash blowup of 2-generic determinantal varieties over fields of positive characteristic is non-singular. We prove this in two steps. Firstly, we explicitly describ…
On the Lipschitz saturation of toric singularities
Daniel Duarte, Arturo E. Giles Flores
We begin the study of Lipschitz saturation for germs of toric singularities. By looking at their associated analytic algebras, we prove that if (X,0) is a germ of toric singularity…