Now showing items 9-28 of 39

• #### 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 ...
• #### 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 ...
• #### 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- ...
• #### 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 ...
• #### On the generalized Nash problem for smooth germs and adjacencies of curve singularities ﻿

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.