A theorem on solutions of analytic equations with applications to deformations of complex structures

DOI10.1007/BF01432540zbMath0303.32018MaRDI QIDQ1216529

John J. Wavrik

Publication date: 1975

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/162731

Mathematics Subject Classification ID

Local analytic geometry (32B99) Deformations of complex structures (32G05) Power series rings (13J05)

Related Items (24)

Isosingular Loci and the Cartesian Product Structure of Complex Analytic Singularities ⋮ Analytic Equations and Singularities of Plane Curves ⋮ Families of arcs on rational surface singularities ⋮ The trivial locus of an analytic map germ ⋮ Ultraproducts and approximation in local rings. II ⋮ Unnamed Item ⋮ The classical Artin approximation theorems ⋮ Artin approximation over Banach spaces ⋮ A note on the one-dimensional systems of formal equations ⋮ Approximation results of Artin-Tougeron-type for general filtrations and for \(C^r\)-equations ⋮ Deformation of complex superspaces and coherent sheaves on them ⋮ A case of affine bound for the Artin approximation function ⋮ Unnamed Item ⋮ Diophantine approximation in power series fields of several variables ⋮ Effective bounds of functions approximating formal solutions of binomial equations ⋮ About the Artin function in dimension \(N\geqslant 2\). ⋮ \(C^k\) and analytic equivalence of complex analytic varieties ⋮ Formal versus analytic CR mappings ⋮ On the nonflatness of analytic tensor product ⋮ Darstellbarkeitskriterien für analytische Funktoren ⋮ Section extension from hyperbolic geometry of punctured disk and holomorphic family of flat bundles ⋮ Sur la linéarité de la fonction de Artin ⋮ Endliche Automorphismengruppen analytischer C-Algebren und ihre Invarianten ⋮ Unnamed Item

Cites Work

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• On the solutions of analytic equations
• Algebraic approximation of structures over complete local rings
• Éléments de géométrie algébrique. I: Le langage des schémas. II: Étude globale élémentaire de quelques classe de morphismes. III: Étude cohomologique des faisceaux cohérents (première partie)
• A Theorem of Completeness for Families of Compact Analytic Spaces
• Deforming Cohomology Classes

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