Now showing items 10-29 of 49

• #### Hölder equivalence of complex analytic curve singularities ﻿

(Bulletin of the London Mathematical Society, 2018-08-06)
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 ...
• #### Intersection cohomology with torus actions of complexity one and intersection space complexes ﻿

(2018-06-18)
• #### 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 $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ...
• #### A Lê-Greuel type formula for the image Milnor number ﻿

(Hokkaido Mathematical Journal, 2019-02)
• #### Mixed tête-à-tête twists as monodromies associated with holomorphic function germs ﻿

(2018-04-01)
Tête-à-tête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed tête-à-tête graphs provide a generalization which define mixed tête-à-tête twists, which ...
• #### Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs ﻿

(2019-10-31)
We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is ...
• #### Monodromies as tête-à-tête graphs ﻿

(2018-05-08)
• #### Multiplicity and degree as bi‐Lipschitz invariants for complex sets ﻿

(Journal of Topology, 2018-08-29)
We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ...
• #### Multiplicity of singularities is not a bi-Lipschitz invariant ﻿

(Mathematische Annalen, 2020-01-17)
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
• #### Multiplicity, regularity and blow-spherical equivalence of complex analytic sets ﻿

(The Asian Journal of Mathematics, 2020-01-29)
This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain several applications with this new ...
• #### The Nash Problem from a Geometric and Topological Perspective ﻿

(2018-04-17)
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- ...
• #### The Nash Problem from Geometric and Topological Perspective ﻿

(WORLD SCIENTIFIC (EUROPE), 2020-03-01)
We survey the proof of the Nash conjecture for surfaces and show how geometric and topological ideas developed in previous articles by the authors influenced it. Later, we summarize the main ideas in the higher dimensional ...
• #### Neron models of intermediate Jacobians associated to moduli spaces ﻿

(Revista Matemática Complutense, 2019-12-01)
Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projective curves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$ with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$ ...
• #### Némethi’s division algorithm for zeta-functions of plumbed 3-manifolds ﻿

(Bulletin of the London Mathematical Society, 2018-08-27)
A polynomial counterpart of the Seiberg-Witten invariant associated with a negative definite plumbing 3-manifold has been proposed by earlier work of the authors. It is provided by a special decomposition of the zeta-function ...
• #### Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds ﻿

(Acta Mathematica Hungarica, 2017-05-18)
We construct a non-normal affine monoid together with its modules associated with a negative definite plumbed 3-manifold 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 ﻿

(2017-01-10)
Classically, there exists a determinant map from the moduli space of semi-stable 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, 2017-05-20)
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 Lipschitz rigidity of complex analytic sets ﻿

(The Journal of Geometric Analysis, 2019-02-26)
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 ...