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mathematics (18) 18
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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
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
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
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
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
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
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
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
Journal Article
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
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 12/1975, Volume 214, pp. 113 - 135
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/1998, Volume 350, Issue 1, pp. 251 - 274
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
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
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 2006, Volume 56, Issue 1, pp. 55 - 85
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
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
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
Journal Article
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