@phdthesis{Hirsch2004, author = {Hirsch, Tobias}, title = {Modular deformations of isolated singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-000000538}, school = {BTU Cottbus - Senftenberg}, year = {2004}, abstract = {In this work, modular subspaces corresponding to the ordinary deformation functor as well as the functor of deformations with section of a singularity. After developing the necessary facts from deformation theory and the techniques of cotangent cohomology, several criteria for modularity are given, in terms of relative cotangent cohomology modules. Based on these theoretical results, an algorithm is explained to obtain the modular stratum of an isolated singularity up to a given order. As applications, the modular strata of isolated hypersurface singularities of small modality are determined and several examples - mainly of (semi-)quasihomogeneous singularities - are presented which exhibit interesting and surprising phenomena.}, subject = {Isolierte Singularit{\"a}t; Deformation ; Computeralgebra; Algebraische Geometrie; Singularit{\"a}tentheorie; Komplexe Analysis; Computeralgebra; Modulr{\"a}ume}, language = {en} }