Now showing items 9-28 of 37

• #### A Jacobian module for disentanglements and applications to Mond's conjecture ﻿

(2017-01-10)
[TBA]
• #### A jacobian module for disentanglements and applications to Mond's conjecture ﻿

(Revista Matemática Complutense, 2019)
Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ...
• #### Logarithmic connections on principal bundles over a Riemann surface ﻿

(arxiv, 2017)
• #### On the generalized Nash problem for smooth germs and adjacencies of curve singularities ﻿

(Advances in Mathematics, 2017-12-10)
In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space ...
• #### On the geometry of strongly flat semigroups and their generalizations ﻿

(2018-09-18)
Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and ...
• #### On Zariski’s multiplicity problem at infinity ﻿

(Proceedings of the American Mathematical Society, 2018-08-14)
We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, ...
• #### Perverse sheaves on semi-abelian varieties -- a survey of properties and applications ﻿

(European Journal of Mathematics, 2019-05)
We survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms ...
• #### A proof of the differentiable invariance of the multiplicity using spherical blowing-up ﻿

(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018-04-21)
In this paper we use some properties of spherical blowing-up to give an alternative and more geometric proof of Gau-Lipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ...
• #### A proof of the integral identity conjecture, II ﻿

(Comptes Rendus Mathematique, 2017-10-31)
In this note, using Cluckers-Loeser’s theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.
• #### Representation of surface homeomorphisms by tête-à-tête graphs ﻿

(2017-06-21)
We use tête-à-tête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with non-empty boundary, improving work of N. A'Campo and C. Graf. We also introduce ...
• #### Right unimodal and bimodal singularities in positive characteristic ﻿

(International Mathematics Research Notices, 2017-08-07)
The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ...