Equianalytic and equisingular families of curves on surfaces

DOI10.1007/BF02567958zbMath0874.14021arXivalg-geom/9503011OpenAlexW2011017991MaRDI QIDQ1353072

Gert-Martin Greuel, Christoph Lossen

Publication date: 13 April 1997

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9503011

zbMATH Keywords

Hilbert schemenumber of singular pointsequianalytic singularityflat families of embedded reduced curvessingularities of given analytic type

Mathematics Subject Classification ID

Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Equisingularity (topological and analytic) (32S15) Singularities of surfaces or higher-dimensional varieties (14J17) Singularities of curves, local rings (14H20)

Related Items

New asymptotics for the existence of plane curves with prescribed singularities, On the equi-normalizable deformations of singularities of complex plane curves, Existence of Hypersurfaces with Prescribed Simple Singularities, Patchworking singular algebraic curves. I, Patchworking singular algebraic curves. II, Geometry of obstructed families of curves, Geometry of families of nodal curves on the blown-up projective plane, Smoothness of equisingular families of curves, Equimultiple deformations of isolated singularities, Irreducibility of equisingular families of curves, On the local deformation space of hypersurfaces of \(\mathbb{P}^n\) with non-isolated singularities, Analytic order of singular and critical points, On the geometric genus of projective curves, Arithmetically Cohen Macaulay embeddings of reducible curves, Versality, Bounds of Global Tjurina Numbers and Logarithmic Vector Fields Along Hypersurfaces with Isolated Singularities, Plane Algebraic Curves with Prescribed Singularities

Cites Work

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• Versal deformations in the space of planar curves of fixed degree
• The semigroup of values of a curve singularity with several branches
• On plane rational curves
• Formal moduli of algebraic structures
• Bifurcations, Dynkin diagrams, and modality of isolated singularities
• Lectures on deformations of singularities. Notes by C. S. Seshadri, Allen Tannenbaum
• Ideals Associated to Deformations of Singular Plane Curves
• Darstellbarkeitskriterien für analytische Funktoren
• Equisingular Deformations of Plane Algebroid Curves
• Deformations of Plane Curves with Nodes and Cusps
• Studies in Equisingularity I Equivalent Singularities of Plane Algebroid Curves
• Functors of Artin Rings
• Lectures on Curves on an Algebraic Surface. (AM-59)