35 citations · 55 across the 11 of their papers we have counts for
11 papers
Classification of singularities of cluster algebras of finite type II: coefficients
Angélica Benito, Eleonore Faber, Hussein Mourtada +1
We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additio…
The asymptotic Samuel function and invariants of singularities
A. Benito, A. Bravo, S. Encinas
The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the S…
Classification of singularities of cluster algebras of finite type: the case of trivial coefficients
Angelica Benito, Eleonore Faber, Hussein Mourtada +1
We provide a complete classification of the singularities of cluster algebras of finite type with trivial coefficients. Alongside, we develop a constructive desingularization of th…
Singularities of locally acyclic cluster algebras
Angélica Benito, Greg Muller, Jenna Rajchgot +1
We show that locally acyclic cluster algebras have (at worst) canonical singularities. In fact, we prove that locally acyclic cluster algebras of positive characteristic are strong…
Measuring Singularities with Frobenius: The Basics
Angélica Benito, Eleonore Faber, Karen E. Smith
Consider a polynomial defined over a field , the multiplicity is perhaps the most naive measurement of the singularities of . This paper describes the first steps toward…
Some natural properties of constructive resolution of singularities
Angélica Benito, Santiago Encinas, Orlando E. Villamayor U
These expository notes, addressed to non-experts, are intended to present some of Hironaka's ideas on his theorem of resolution of singularities. We focus particularly on those asp…
On elimination of variables in the study of singularities in positive characteristic
Angélica Benito, Orlando E. Villamayor
The objective of this paper is to discuss invariants of singularities of algebraic schemes over fields of positive characteristic, and to show how they yield the simplification of…
Techniques for the study of singularities with applications to resolution of 2-dimensional schemes
Angélica Benito, Orlando E. Villamayor
We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimen…
Monoidal transforms and invariants of singularities in positive characteristic
Angélica Benito, Orlando E. Villamayor
The problem of resolution of singularities in positive characteristic can be reformulated as follows: Fix a hypersurface , embedded in a smooth scheme, with points of multiplici…
The -invariant and elimination
Angélica Benito
In this paper we present some results showing the good behavior of the -invariant of a Rees algebra with integral closure and elimination (of variables).
Monoidal transformations of singularities in positive characteristic
Angélica Benito, Orlando Villamayor
A sequence of monoidal transformations is defined, in terms of invariants, for a singular hypersurface embedded in a smooth scheme of positive characteristic. Some examples are add…