Browsing Singularity Theory and Algebraic Geometry by Issue Date
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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 ... 
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 ... 
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, ... 
Monodromies as têteàtête graphs
(20180508) 
Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3manifolds
(201806)Assume that the link of a complex normal surface singularity is a rational homology sphere. Then its SeibergWitten invariant can be computed as the ‘periodic constant’ of the topological multivariable Poincaré series (zeta ... 
Singularities in Geometry and Topology
(20180618)This thesis consists of two different topics that are not related. The thesis has two different and independent parts that can be read in any order. The purpose of this work is to study two topics in singularity theory: ... 
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 ... 
Hölder equivalence of complex analytic curve singularities
(Bulletin of the London Mathematical Society, 20180806)We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$H\"older ... 
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, ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(20180819)In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ... 
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 ... 
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 ... 
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 ... 
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)$, ... 
A LêGreuel type formula for the image Milnor number
(Hokkaido Mathematical Journal, 201902)Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n1},0)\to ... 
On Lipschitz rigidity of complex analytic sets
(The Journal of Geometric Analysis, 20190226)We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ... 
Examples of varieties with index one on C1 fields
(Journal of Number Theory, 20190416)Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1. 
Perverse sheaves on semiabelian varieties  a survey of properties and applications
(European Journal of Mathematics, 201905)We survey recent developments in the study of perverse sheaves on semiabelian varieties. As concrete applications, we discuss various restrictions on the homotopy type of complex algebraic manifolds (expressed in terms ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(Contemporary Mathematics, 20190528)In this paper we present some applications of A'CampoLê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones ...