4 papers · 1 filter
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…