We introduce the concept of a good Saito basis for a plane curve and we explore it to obtain
a formula for the minimal Tjurina number in a topological class. In particular, we give a lower …

We give a survey on some aspects of deformations of isolated singularities. In addition to the
presentation of the general theory, we report on the question of the smoothability of a …

In this paper we give a complete answer to a question posed by Dimca and Greuel about the
quotient of the Milnor and Tjurina numbers of a plane curve singularity. We put this question …

Polar germs, Jacobian ideal and analytic classification of irreducible plane curve singularities |
manuscripta mathematica Skip to main content SpringerLink Account Menu Find a journal …

We study the Jacobian scheme of a plane algebraic curve at an ordinary singularity,
characterizing it through a geometric property. We give an algorithm that gives the analytic …

In this note, we provide a formula for the Tjurina number of a join of isolated hypersurface
singularities in separated variables. From this, we are able to provide a characterization of …

The value semigroup of a k-semiroot C k of a plane branch C allows us to recover part of the
value semigroup Γ=< v 0,…, vg> of C, that is, it is related to topological invariants of C. In this …

arXiv:2501.12836v1 [math.AG] 22 Jan 2025 Page 1 arXiv:2501.12836v1 [math.AG] 22 Jan
2025 THE TJURINA NUMBER OF A PLANE CURVE WITH TWO BRANCHES AND HIGH …

We prove that the numerical invariant 3 μ− 4 τ of a reduced irreducible plane curve
singularity germ is non-negative, non-decreasing under blowups and strictly increasing …

Let $\mathcal {F} $ be a holomorphic foliation at $ p\in\mathbb {C}^ 2$, and $ B $ be a
separatrix of $\mathcal {F} $. We prove the following Dimca-Greuel type inequality $\frac …