Browsing Singularity Theory and Algebraic Geometry by Title
Now showing items 2039 of 60

A LêGreuel type formula for the image Milnor number
(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 ... 
Local Topological Obstruction For Divisors
(2020)Given a smooth, projective variety $X$ and an effective divisor $D\,\subseteq\, X$, it is wellknown that the (topological) obstruction to the deformation of the fundamental class of $D$ as a Hodge class, lies in ... 
Logarithmic connections on principal bundles over a Riemann surface
(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 ... 
Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs
(20191031)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 têteàtête graphs
(20180508) 
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
(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 ... 
Multiplicity of singularities is not a biLipschitz invariant
(20200117)It was conjectured that multiplicity of a singularity is biLipschitz invariant. We disprove this conjecture constructing examples of biLipschitz equivalent complex algebraic singularities with different values of multiplicity. 
Multiplicity, regularity and blowspherical equivalence of complex analytic sets
(20200129)This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blowspherical equivalence and we obtain several applications with this new ... 
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 ... 
The Nash Problem from Geometric and Topological Perspective
(20200301)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 zetafunctions of plumbed 3manifolds
(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 ... 
Neron models of intermediate Jacobians associated to moduli spaces
(20191201)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 $\mathcal{X}$ ... 
Nonnormal affine monoids, modules and Poincaré series of plumbed 3manifolds
(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 a conjecture of harris
(2019)For d ≥ 4, the NoetherLefschetz 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
(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 Lipschitz rigidity of complex analytic sets
(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 ... 
On the generalized Nash problem for smooth germs and adjacencies of curve singularities
(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 ...