Mathematische Nachrichten, ISSN 0025-584X, 03/2020, Volume 293, Issue 3, pp. 475 - 490

We relate the equianalytic and the equisingular deformations of a reduced complex plane curve to the Jacobian syzygies of its defining equation...

equisingular deformation | Jacobian ideal | nearly free curve | free curve | equianalytic deformation | equisingular ideal | Primary: 14H50; Secondary: 14B05 | 13D10 | rational cuspidal curve | 14C05 | 13D02 | Secondary | NUMBER | SERIES | MATHEMATICS | Primary | EQUISINGULAR FAMILIES | GEOMETRY | Algebraic Geometry | Mathematics

equisingular deformation | Jacobian ideal | nearly free curve | free curve | equianalytic deformation | equisingular ideal | Primary: 14H50; Secondary: 14B05 | 13D10 | rational cuspidal curve | 14C05 | 13D02 | Secondary | NUMBER | SERIES | MATHEMATICS | Primary | EQUISINGULAR FAMILIES | GEOMETRY | Algebraic Geometry | Mathematics

Journal Article

Mathematische Nachrichten, ISSN 1522-2616, 2006, Volume 279, Issue 7, pp. 716 - 726

The goal of this paper is to give a method to compute the space of infinitesimal deformations of a double cover of a smooth algebraic variety...

Equisingular deformations | double coverings | Double coverings | CALABI-YAU THREEFOLDS | MATHEMATICS | COUNTEREXAMPLES | SINGULARITIES | equisingular deformations | TORELLI PROBLEM | CURVE

Equisingular deformations | double coverings | Double coverings | CALABI-YAU THREEFOLDS | MATHEMATICS | COUNTEREXAMPLES | SINGULARITIES | equisingular deformations | TORELLI PROBLEM | CURVE

Journal Article

Publicacions matemàtiques, ISSN 0214-1493, 2017, Volume 61, Issue 1, pp. 175 - 212

We investigate the following question: let C be an integral curve contained in a smooth complex algebraic surface X; is it possible to deform C in X into a...

Equigeneric and equi- singular deformations | Nodal curves | Families of singular curves on algebraic surfaces | MATHEMATICS | equigeneric and equisingular deformations | NODES | NUMBER | SEVERI VARIETIES | DIVISORS | K3 SURFACES | DEFORMATIONS | RATIONAL CURVES | nodal curves | PLANE-CURVES

Equigeneric and equi- singular deformations | Nodal curves | Families of singular curves on algebraic surfaces | MATHEMATICS | equigeneric and equisingular deformations | NODES | NUMBER | SEVERI VARIETIES | DIVISORS | K3 SURFACES | DEFORMATIONS | RATIONAL CURVES | nodal curves | PLANE-CURVES

Journal Article

Compositio mathematica, ISSN 0010-437X, 7/2007, Volume 143, Issue 4, pp. 829 - 882

The purpose of this paper is to develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic...

Deformation of parametrization | Hamburger-Noether expansion | Milnor number | Equisingular deformation | Plane curve singularities | MATHEMATICS | SINGULARITIES | Mathematical problems | Theory

Deformation of parametrization | Hamburger-Noether expansion | Milnor number | Equisingular deformation | Plane curve singularities | MATHEMATICS | SINGULARITIES | Mathematical problems | Theory

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2018, Volume 68, Issue 2, pp. 725 - 766

We consider the germ of a reduced curve, possibly reducible. F. Delgado de la Mata proved that such a curve is Gorenstein if and only if its semigroup of...

Gorenstein curves | Values | Duality | Logarithmic residues | Equisingular deformations | SEMIGROUP | MATHEMATICS | logarithmic residues | MODULES | ANALYTIC CLASSIFICATION | HYPERSURFACES | values | equisingular deformations | SINGULARITY | DIFFERENTIALS | duality

Gorenstein curves | Values | Duality | Logarithmic residues | Equisingular deformations | SEMIGROUP | MATHEMATICS | logarithmic residues | MODULES | ANALYTIC CLASSIFICATION | HYPERSURFACES | values | equisingular deformations | SINGULARITY | DIFFERENTIALS | duality

Journal Article

Topology and its applications, ISSN 0166-8641, 2002, Volume 118, Issue 1-2, pp. 31 - 43

We consider surface singularities in C 3 arising as the total space of an equisingular deformation of an isolated curve singularity of the form f( x, y)+ zg( x, y...

Equisingular deformation | Logarithmic derivation | Nonisolated singularity | Free divisor | free divisor | nonisolated singularity | MATHEMATICS | equisingular deformation | MATHEMATICS, APPLIED | logarithmic derivation | DISCRIMINANTAL ARRANGEMENTS | VECTOR-FIELDS

Equisingular deformation | Logarithmic derivation | Nonisolated singularity | Free divisor | free divisor | nonisolated singularity | MATHEMATICS | equisingular deformation | MATHEMATICS, APPLIED | logarithmic derivation | DISCRIMINANTAL ARRANGEMENTS | VECTOR-FIELDS

Journal Article

Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, 11/2003, Volume 135, Issue 3, pp. 385 - 394

A sufficient condition for the equisingularity of inverse images of plane curve singularities, as well as a formula for their Milnor numbers, are given.

MATHEMATICS | EQUISINGULAR DEFORMATIONS | EXPANSIONS

MATHEMATICS | EQUISINGULAR DEFORMATIONS | EXPANSIONS

Journal Article

Journal of Symbolic Computation, ISSN 0747-7171, 2007, Volume 42, Issue 1, pp. 89 - 114

We present an algorithm which, given a deformation with section of a reduced plane curve singularity, computes equations for the equisingularity stratum (that is, the...

Hamburger–Noether expansion | Deformation of parametrization | Milnor number | Equisingular deformation | Plane curve singularities | Hamburger-Noether expansion | equisingular deformation | MATHEMATICS, APPLIED | RINGS | COMPUTER SCIENCE, THEORY & METHODS | plane curve singularities | deformation of parametrization | Algorithms

Hamburger–Noether expansion | Deformation of parametrization | Milnor number | Equisingular deformation | Plane curve singularities | Hamburger-Noether expansion | equisingular deformation | MATHEMATICS, APPLIED | RINGS | COMPUTER SCIENCE, THEORY & METHODS | plane curve singularities | deformation of parametrization | Algorithms

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 01/2005, Volume 249, Issue 1, pp. 31 - 62

Journal Article

Publicacions Matematiques, ISSN 0214-1493, 2017, Volume 61, Issue 1, pp. 175 - 212

Journal Article

Proceedings of the Japan Academy Series A: Mathematical Sciences, ISSN 0386-2194, 1999, Volume 75, Issue 7, pp. 99 - 102

... on S. In this paper we shall give a description of the cohomology H-1(S, Theta(s)), which is called the infinitesimal locally trivial deformation space of S, using a 2-cubic hyper-resolution of S in the sense of F. Guillen, V...

MATHEMATICS | HYPER-EQUISINGULAR FAMILIES | PROJECTIVE VARIETIES

MATHEMATICS | HYPER-EQUISINGULAR FAMILIES | PROJECTIVE VARIETIES

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/1975, Volume 214, pp. 113 - 135

Parametrizations of a deformation (over a complete local ring) of an irreducible algebroid curve are studied...

Integers | Homomorphisms | Tangents | Algebra | Mathematical theorems | Semigroups | Functors | Mathematical rings | Power series | Versal deformation | Deformation parametrization | Characteristic of а parametrization | Equisingular deformation | Branch | P-truncation of а family | Formal family of branches | Puiseux expansion

Integers | Homomorphisms | Tangents | Algebra | Mathematical theorems | Semigroups | Functors | Mathematical rings | Power series | Versal deformation | Deformation parametrization | Characteristic of а parametrization | Equisingular deformation | Branch | P-truncation of а family | Formal family of branches | Puiseux expansion

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 01/1998, Volume 350, Issue 1, pp. 251 - 274

Let \mathbb P^2_r be the projective plane blown up at r generic points. De\-note by {E_0,E_1,\ldots ,E_r} the strict transform of a generic straight line on...

Linear systems | Integers | Algebra | Mathematical induction | Plane curves | Geometric planes | Mathematical surfaces | Curves | Induction assumption | Nodal curves | Equisingular deformation | Families of curves | Existence | Nodes | Blown-up projective space | MATHEMATICS | equisingular deformation | NUMBER | nodes | PRESCRIBED SINGULARITIES | families of curves | ALGEBRAIC-CURVES | existence | blown-up projective space | nodal curves | SURFACES | CONJECTURE

Linear systems | Integers | Algebra | Mathematical induction | Plane curves | Geometric planes | Mathematical surfaces | Curves | Induction assumption | Nodal curves | Equisingular deformation | Families of curves | Existence | Nodes | Blown-up projective space | MATHEMATICS | equisingular deformation | NUMBER | nodes | PRESCRIBED SINGULARITIES | families of curves | ALGEBRAIC-CURVES | existence | blown-up projective space | nodal curves | SURFACES | CONJECTURE

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 8/1976, Volume 221, Issue 2, pp. 303 - 321

... only locally trivial deformations of pairs of schemes over local artin k-algebras. The functor of locally trivial deformations of the formal embedding of an exceptional set has a versal object in the sense of Schlessinger...

Morphisms | Integers | Algebra | Deformation | Mathematical theorems | Functors | Mathematical rings | Topology | Topological spaces | Locally complete intersection | Deformation of a pair | Equisingular deformation | Formally embedded exceptional set | Formal moduli

Morphisms | Integers | Algebra | Deformation | Mathematical theorems | Functors | Mathematical rings | Topology | Topological spaces | Locally complete intersection | Deformation of a pair | Equisingular deformation | Formally embedded exceptional set | Formal moduli

Journal Article

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 2001, Volume 2001, Issue 11, pp. 543 - 550

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/1998, Volume 126, Issue 1, pp. 25 - 34

This paper studies the moduli space corresponding to irreducible germs of plane analytic curve with a single characteristic exponent. We stratify the moduli...

Integers | Equivalence relation | Exponents | Plane curves | Geometric planes | Coordinate systems | Semigroups | Cocoa | Jacobians | Moduli | Tjurina number | Equisingular miniversal deformation | MATHEMATICS | MATHEMATICS, APPLIED | moduli | equisingular miniversal deformation

Integers | Equivalence relation | Exponents | Plane curves | Geometric planes | Coordinate systems | Semigroups | Cocoa | Jacobians | Moduli | Tjurina number | Equisingular miniversal deformation | MATHEMATICS | MATHEMATICS, APPLIED | moduli | equisingular miniversal deformation

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 2006, Volume 56, Issue 1, pp. 55 - 85

This is a survey of our results on the relation between perturbative renormalization and motivic Galois theory. The main result is that all quantum field...

Motives | Equisingular connections | Irregular Riemann–Hilbert correspondence | Motivic Galois groups | Hopf algebras and affine group schemes | Perturbative renormalization | Irregular Riemann-Hilbert correspondence | MATHEMATICS | motivic Galois groups | motives | RIEMANN-HILBERT PROBLEM | irregular Riemann-Hilbert correspondence | equisingular connections | PHYSICS, MATHEMATICAL | perturbative renormalization | RENORMALIZATION

Motives | Equisingular connections | Irregular Riemann–Hilbert correspondence | Motivic Galois groups | Hopf algebras and affine group schemes | Perturbative renormalization | Irregular Riemann-Hilbert correspondence | MATHEMATICS | motivic Galois groups | motives | RIEMANN-HILBERT PROBLEM | irregular Riemann-Hilbert correspondence | equisingular connections | PHYSICS, MATHEMATICAL | perturbative renormalization | RENORMALIZATION

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2019, Volume 147, Issue 10, pp. 4233 - 4244

Let (S,L) be a polarized K3 surface of genus p \geq 11 such that {\rm Pic}(S)=\mathbf {Z}[L] and \delta is a non-negative integer. We prove that if p\geqslant...

MATHEMATICS | MATHEMATICS, APPLIED | RATIONAL CURVES | PARAMETER SPACES | DIVISORS | EQUISINGULAR FAMILIES | Algebraic Geometry | Mathematics

MATHEMATICS | MATHEMATICS, APPLIED | RATIONAL CURVES | PARAMETER SPACES | DIVISORS | EQUISINGULAR FAMILIES | Algebraic Geometry | Mathematics

Journal Article

Proceedings of the Indian Academy of Sciences - Mathematical Sciences, ISSN 0253-4142, 8/2002, Volume 112, Issue 3, pp. 383 - 391

A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus...

Mathematics, general | Mathematics | Equisingular | geometrically rigid | Geometrically rigid | MATHEMATICS | equisingular

Mathematics, general | Mathematics | Equisingular | geometrically rigid | Geometrically rigid | MATHEMATICS | equisingular

Journal Article

Communications in Algebra, ISSN 0092-7872, 02/2005, Volume 33, Issue 2, pp. 455 - 466

In Keilen ( 2003 ) we gave sufficient conditions for the irreducibility of the family of irreducible curves in the linear system |D| l with precisely r...

Secondary 14J26 | Primary 14H10 | Singularity theory | Equisingular families of curves | Algebraic geometry | MATHEMATICS | singularity theory | algebraic geometry | equisingular families of curves | SURFACES

Secondary 14J26 | Primary 14H10 | Singularity theory | Equisingular families of curves | Algebraic geometry | MATHEMATICS | singularity theory | algebraic geometry | equisingular families of curves | SURFACES

Journal Article

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