03420nam 22006975 450 991014463370332120211103164418.03-540-36464-110.1007/b10723(CKB)1000000000229462(SSID)ssj0000322493(PQKBManifestationID)12072434(PQKBTitleCode)TC0000322493(PQKBWorkID)10286968(PQKB)10520752(DE-He213)978-3-540-36464-1(MiAaPQ)EBC6286397(MiAaPQ)EBC5610695(Au-PeEL)EBL5610695(OCoLC)52371127(PPN)155167138(EXLCZ)99100000000022946220121227d2003 u| 0engurnn#008mamaatxtccrDeformations of Singularities[electronic resource] /by Jan Stevens1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (X, 166 p.)Lecture Notes in Mathematics,0075-8434 ;1811Bibliographic Level Mode of Issuance: Monograph3-540-00560-9 Introduction -- Deformations of singularities -- Standard bases -- Infinitesimal deformations -- Example: the fat point of multiplicity four -- Deformations of algebras -- Formal deformation theory -- Deformations of compact manifolds -- How to solve the deformation equation -- Convergence for isolated singularities -- Quotient singularities -- The projection method -- Formats -- Smoothing components of curves -- Kollár's conjectures -- Cones over curves -- The versal deformation of hyperelliptic cones -- References -- Index.These notes deal with deformation theory of complex analytic singularities and related objects. The first part treats general theory. The central notion is that of versal deformation in several variants. The theory is developed both in an abstract way and in a concrete way suitable for computations. The second part deals with more specific problems, specially on curves and surfaces. Smoothings of singularities are the main concern. Examples are spread throughout the text.Lecture Notes in Mathematics,0075-8434 ;1811Differential geometryFunctions of complex variablesAlgebraic geometryDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Several Complex Variables and Analytic Spaceshttps://scigraph.springernature.com/ontologies/product-market-codes/M12198Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Differential geometry.Functions of complex variables.Algebraic geometry.Differential Geometry.Several Complex Variables and Analytic Spaces.Algebraic Geometry.516.3532S25msc32S30mscStevens Janauthttp://id.loc.gov/vocabulary/relators/aut67452MiAaPQMiAaPQMiAaPQBOOK9910144633703321Deformations of singularities145368UNINA