Browsing Singularity Theory and Algebraic Geometry by Title
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Parametrization simple irreducible plane curve singularities in arbitrary characteristic
(20200101)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 ... 
Perverse sheaves on semiabelian varieties  a survey of properties and applications
(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
(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
(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. 
Reflection maps
(2020)Given a reflection group G acting on a complex vector space V , a reflection map is the composition of an embedding X → V with the quotient map V → Cp of G. We show how these maps, which can highly singular, may be studied ... 
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
(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
(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
(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: ... 
Singularities of the Hilbert scheme of effective divisors
(20170110)In this article, we study the Hilbert scheme of effective divisors in smooth hypersurfaces in $\mathbb{P}^3$, a topic not extensively studied. We prove that there exists such effective divisors $D$ satisfying the property: ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(20180819)In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(20190528)In this paper we present some applications of A'CampoLê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent cones ... 
Some classes of homeomorphisms that preserve multiplicity and tangent cones
(20200101)In this paper we present some applications of A’CampoLˆe’s Theorem and we study some relations between Zariski’s Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent ... 
Some contributions to the theory of singularities and their characteristic classes
(20210602)In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ... 
A specialization property of index
(20170110)In [Kol13] Kollár defined $i$th index of a proper scheme over a field. In this note we study how index behaves under specialization, in any characteristic. 
Surgery formulae for the SeibergWitten invariant of plumbed 3manifolds
(201702)Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincar\'e series associated ... 
Topological invariants of plane curve singularities: Polar quotients and Lojasiewicz gradient exponents
(20191021)In this paper, we study polar quotients and Łojasiewicz exponents of plane curve singularities, which are not necessarily reduced. We first show that, for complex plane curve singularities, the set of polar quotients is a ... 
Topology of Spaces of Valuations and Geometry of Singularities
(20171111)Given an algebraic variety X defined over an algebraically closed field, we study the space RZ(X,x) consisting of all the valuations of the function field of X which are centered in a closed point x of X. We concentrate ...