3 papers
math.AC2026
n-trivial extensions and multi Hasse-Schmidt derivations
Paul Barajas, Daniel Duarte
We propose a generalization of Hasse-Schmidt derivations that is equivalent to the notion of n-trivial extension introduced by Anderson-Bennis-Fahid-Shaiea, in the same way that de…
math.AG2025
The blow-up of a singularity at the module of derivations
Paul Barajas, Enrique Chávez-Martínez, Agustín Romano-Velázquez
We study the problem of resolving singularities via the blow-up of the module of derivations. Our main results are a positive answer for the case of curves and log-canonical surfac…
math.AC2018
On the module of differentials of order of hypersurfaces
Paul Barajas, Daniel Duarte
We give an explicit presentation of the module of differentials of order of a finitely generated algebra via a higher-order Jacobian matrix. We use the presentation to study so…