Browsing Singularity Theory and Algebraic Geometry by Title
Now showing items 2241 of 49

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
(WORLD SCIENTIFIC (EUROPE), 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 ... 
Neron models of intermediate Jacobians associated to moduli spaces
(Revista Matemática Complutense, 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 $\mathcal{X}$ ... 
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 ... 
Nonnormal affine monoids, modules and Poincaré series of plumbed 3manifolds
(Acta Mathematica Hungarica, 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 intersection cohomology with torus actions of complexity one
(Revista Matemática Completense, 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
(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 ... 
On the generalized Nash problem for smooth germs and adjacencies of curve singularities
(Advances in Mathematics, 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 ... 
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, ... 
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 ... 
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, ... 
A proof of the integral identity conjecture, II
(Comptes Rendus Mathematique, 20171031)In this note, using CluckersLoeser’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. 
Representation of surface homeomorphisms by têteàtête graphs
(20170621)We use têteàtête graphs as defined by N. A'campo and extended versions to codify all periodic mapping classes of an orientable surface with nonempty boundary, improving work of N. A'Campo and C. Graf. We also introduce ... 
Right unimodal and bimodal singularities in positive characteristic
(International Mathematics Research Notices, 20170807)The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ... 
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 ... 
A Short Survey on the Integral Identity Conjecture and Theories of Motivic Integration
(Acta Mathematica Vietnamica, 20170404)In KontsevichSoibelman’s theory of motivic DonaldsonThomas invariants for 3dimensional noncommutative CalabiYau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ... 
A Short Survey on the Integral Identity Conjectureand Theories of Motivic Integration
(Acta Mathematica Vietnamica, 20161216)In KontsevichSoibelman’s theory of motivic DonaldsonThomas invariants for 3dimensional noncommutative CalabiYau varieties, the integral identity conjecture plays a crucial role as it involves the existence of these ... 
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: ...