4 papers
On a Computational Approach to the Nash Blowup Problem
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Ãlvarez +2
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…
Nash blowup fails to resolve singularities in dimensions four and higher
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Ãlvarez +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…
Non-normalized Nash blowup fails to resolve singularities in dimension three
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Ãlvarez +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…
Characteristic-free normalized Nash blowup of toric varieties
Federico Castillo, Daniel Duarte, Maximiliano Leyton-Ãlvarez +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…