Browsing Singularity Theory and Algebraic Geometry by Title
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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)Let $E_G$ be a holomorphic principal $G$bundle on a compact connected Riemann surface $X$, where $G$ is a connected reductive complex affine algebraic group. Fix a finite subset $D\, \subset\, X$, and for each $x\,\in\, ... 
Mixed têteàtête twists as monodromies associated with holomorphic function germs
(20180401)Têteàtête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed têteàtête graphs provide a generalization which define mixed têteàtête twists, which ... 
Monodromies as têteàtête graphs
(20180508) 
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
(Journal of Topology, 20180829)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer biLipschitz transformations (outer biLipschitz homeomorphims of germs in the first case and outer biLipschitz ... 
The Nash Problem from a Geometric and Topological Perspective
(20180417)We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the au thors influenced it. Later we summarize the main ideas in the higher dimen ... 
Némethi’s division algorithm for zetafunctions of plumbed 3manifolds
(Bulletin of the London Mathematical Society, 20180827)A polynomial counterpart of the SeibergWitten invariant associated with a negative definite plumbing 3manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zetafunction ... 
Nonnormal affine monoids, modules and Poincaré series of plumbed 3manifolds
(Acta Mathematica Hungarica, 20170518)We construct a nonnormal affine monoid together with its modules associated with a negative definite plumbed 3manifold M. In terms of their structure, we describe the $H_1(M,\mathbb{Z})$equivariant parts of the topological ... 
A note on the determinant map
(20170110)Classically, there exists a determinant map from the moduli space of semistable sheaves on a smooth, projective variety to the Picard scheme. Unfortunately, if the underlying variety is singular, then such a map does not ... 
On intersection cohomology with torus actions of complexity one
(Revista Matemática Completense, 20170520)The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus T, one of our result determines the intersection cohomology Betti numbers of ... 
On the generalized Nash problem for smooth germs and adjacencies of curve singularities
(Advances in Mathematics, 20171210)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
(20180918)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, 20180814)We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are biLipschitz homeomorphic at infinity must have the same degree. More specifically, ... 
A proof of the differentiable invariance of the multiplicity using spherical blowingup
(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 20180421)In this paper we use some properties of spherical blowingup to give an alternative and more geometric proof of GauLipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ... 
A proof of the integral identity conjecture, II
(Comptes Rendus Mathematique, 20171031)In this note, using CluckersLoeser’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 têteàtête graphs
(20170621)We use têteàtête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with nonempty 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, 20170807)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 ... 
Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities
(20180630)In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ... 
A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration
(Acta Mathematica Vietnamica, 20170404)In KontsevichSoibelman’s theory of motivic DonaldsonThomas invariants for 3dimensional noncommutative CalabiYau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ...