Maximiliano Leyton-'Alvarez

activity

20142025

μ

-constant deformations admit simultaneous embedded resolutions

5 citations · 5 across the 10 of their papers we have counts for

collaborators

13 papers

math.AG2025

$Z_{p}^{m}$ -actions of type $(d; p, n)$

Ruben A. HIdalgo, Maximiliano Leyton-Alvarez

A $Z_{p}^{m}$ -action of type $(d; p, n)$ , where $2 \leq d \leq m \leq n$ are integers, is a pair $(S, N)$ where $S$ is a $d$ -dimensional compact complex manifold, $N \cong {…

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

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…

math.AG2025

Jet Schemes, Newton Polygons and Continued Fractions

Ghadi Abdallah, Maximiliano Leyton-Álvarez, Bassam Mourad +1

We study jet schemes of Newton non-degenerate plane curve singularities. We identify a subgraph of the graph of jet components and show that it can be constructed from walks on the…

math.AG2025

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…

math.AG2024

Uniqueness of Generalized Fermat Groups in positive characteristic

Rubén A. Hidalgo, Henry F. Hughes, Maximiliano Leyton-Álvarez

Let $X \subset P_{K}^{m}$ be a smooth irreducible projective algebraic variety of dimension $d$ , defined over an algebraically closed field $K$ of characteristic $p > 0$ . We…

math.AG2024

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.AG2020

Automorphisms of Generalized Fermat manifolds

Ruben A. Hidalgo, Henry F. Hughes, Maximiliano Leyton-Alvarez

Let $d \geq 1$ , $k \geq 2$ and $n \geq d + 1$ be integers. A $d$ -dimensional smooth complex algebraic variety $M$ is called a generalized Fermat variety of type $(d; k, n)$ if there is…

math.AG2020★ 5 cited

Newton non-degenerate $μ$ -constant deformations admit simultaneous embedded resolutions

Maximiliano Leyton-Álvarez, Hussein Mourtada, Mark Spivakovsky

Let $C_{o}^{n + 1}$ denote the germ of $C^{n + 1}$ at the origin. Let $V$ be a hypersurface germ in $C_{o}^{n + 1}$ and $W$ a deformation of $V$ over $\mathbb{C}_{…

math.AG2018

Weierstrass weight of the hyperosculating points of generalized Fermat curves

Rubén A. Hidalgo, Maximiliano Leyton-Álvarez

Let $(S, H)$ be a generalized Fermat pair of the type $(k, n)$ . If $F \subset S$ is the set of fixed points of the non-trivial elements of the group $H$ , then $F$ is exactly the set o…

math.AG2015

Deforming spaces of m-jets of hypersurfaces singularities

Maximiliano Leyton-Álvarez

Let $K$ be an algebraically closed field of characteristic zero, and $V$ a hypersurface defined by an irreducible polynomial $f$ with coefficients in $K$ . In thi…

math.AG2014

Weierstrass weight of the hyperosculating points of generalized Fermat curves

Rubén A. Hidalgo, Maximiliano Leyton-Álvarez

Let $(S, H)$ be a generalized Fermat pair of the type $(k, n)$ . If $F \subset S$ is the set of fixed points of the non-trivial elements of the group $H$ , then $F$ is exactly the set o…

math.AG2014

Automorphisms of the Generalized Fermat curves

Rubén A. Hidalgo, Aristides Kontogeorgis, Maximiliano Leyton-Álvarez +1

Let $K$ be an algebraically closed field of characteristic $p \geq 0$ . A generalized Fermat curve of type $(k, n)$ , where $k, n \geq 2$ are integers (for $p \neq = 0$ we also assume th…

Zpm​-actions of type (d;p,n)

Non-normalized Nash blowup fails to resolve singularities in dimension three

On a Computational Approach to the Nash Blowup Problem

Jet Schemes, Newton Polygons and Continued Fractions

Characteristic-free normalized Nash blowup of toric varieties

Uniqueness of Generalized Fermat Groups in positive characteristic

Nash blowup fails to resolve singularities in dimensions four and higher

Automorphisms of Generalized Fermat manifolds

Newton non-degenerate μ-constant deformations admit simultaneous embedded resolutions

Weierstrass weight of the hyperosculating points of generalized Fermat curves

Deforming spaces of m-jets of hypersurfaces singularities

Weierstrass weight of the hyperosculating points of generalized Fermat curves

Automorphisms of the Generalized Fermat curves

$Z_{p}^{m}$ -actions of type $(d; p, n)$

Newton non-degenerate $μ$ -constant deformations admit simultaneous embedded resolutions