Deformations of Singularities
Stevens, Jan.
Deformations of Singularities [electronic resource] / by Jan Stevens. - X, 166 p. online resource. - Lecture Notes in Mathematics, 1811 0075-8434 ; . - Lecture Notes in Mathematics, 1811 .
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.
9783540364641
10.1007/b10723 doi
Global differential geometry.
Differential equations, partial.
Geometry, algebraic.
Differential Geometry.
Several Complex Variables and Analytic Spaces.
Algebraic Geometry.
QA641-670
516.36
Deformations of Singularities [electronic resource] / by Jan Stevens. - X, 166 p. online resource. - Lecture Notes in Mathematics, 1811 0075-8434 ; . - Lecture Notes in Mathematics, 1811 .
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.
9783540364641
10.1007/b10723 doi
Global differential geometry.
Differential equations, partial.
Geometry, algebraic.
Differential Geometry.
Several Complex Variables and Analytic Spaces.
Algebraic Geometry.
QA641-670
516.36