collaborators

7 papers

math.AG2026

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…

math.AG2025

On a Computational Approach to the Nash Blowup Problem

Federico Castillo, Daniel Duarte, Maximiliano Leyton-Álvarez +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…

math.AG2025

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…

math.AG2025

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…

math.AG2025

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…

math.AG2025

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…