Now showing items 30-49 of 70

• #### 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 ...
• #### Moderately Discontinuous Homology ﻿

(2021-01-01)
We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ...
• #### Monodromies as tête-à-tête graphs ﻿

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

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### Némethi’s division algorithm for zeta-functions of plumbed 3-manifolds ﻿

(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 ...
• #### Neron models of intermediate Jacobians associated to moduli spaces ﻿

(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 $\mathcal{X}$ ...
• #### Non-normal affine monoids, modules and Poincaré series of plumbed 3-manifolds ﻿

(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 a conjecture of harris ﻿

(2019)
For d ≥ 4, the Noether-Lefschetz locus NLd parametrizes smooth, degree d sur- faces in P3 with Picard number at least 2. A conjecture of Harris states that there are only finitely many irreducible components of the ...
• #### On intersection cohomology with torus actions of complexity one ﻿

(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 ﻿

(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 ﻿

(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 the length of perverse sheaves on hyperplane arrangements ﻿

(2019)
Abstract. In this article we address the length of perverse sheaves arising as direct images of rank one local systems on complements of hyperplane arrangements. In the case of a cone over an essential line arrangement ...
• #### On Zariski’s multiplicity problem at infinity ﻿

(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, ...
• #### Parametrization simple irreducible plane curve singularities in arbitrary characteristic ﻿

(2020-01-01)
We study the classification of plane curve singularities in arbitrary characteristic. We first give a bound for the determinacy of a plane curve singularity with respect to pararametrization equivalence in terms of its ...