國立虎尾科技大學 |

Singularities of Mappings = The Local Behaviour of Smooth and Complex Analytic Mappings /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Singularities of Mappings/ by David Mond, Juan J. Nuño-Ballesteros.
Reminder of title:	The Local Behaviour of Smooth and Complex Analytic Mappings /
Author:	Mond, David.
other author:	Nuño-Ballesteros, Juan J.
Description:	XV, 567 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebraic geometry. -
Online resource:	https://doi.org/10.1007/978-3-030-34440-5
ISBN:	9783030344405

Singularities of Mappings = The Local Behaviour of Smooth and Complex Analytic Mappings /
Mond, David.

Singularities of MappingsThe Local Behaviour of Smooth and Complex Analytic Mappings /[electronic resource] :by David Mond, Juan J. Nuño-Ballesteros. - 1st ed. 2020. - XV, 567 p.online resource. - Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,3570072-7830 ;. - Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,351.

Introduction -- Part I Thom-Mather Theory: Right-Left Equivalence, Stability,Versal Unfoldings, Finite Determinacy -- Manifolds and Smooth Mappings -- Left-Right Equivalence and Stability -- Contact Equivalence -- Versal Unfoldings -- Finite Determinacy -- Classification of Stable Germs by Their Local Algebras -- Part II Images and Discriminants: The Topology of Stable Perturbations -- Stable Images and Discriminants -- Multiple Points -- Calculating the Homology of the Image -- Multiple Points in the Target: The Case of Parameterised Hypersurfaces -- Appendix A: Jet Spaces and Jet Bundles -- Appendix B Stratifications -- Appendix C Background in Commutative Algebra -- Appendix D Local Analytic Geometry -- Appendix E Sheaves. References -- Index.

The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.

ISBN: 9783030344405

Standard No.: 10.1007/978-3-030-34440-5doiSubjects--Topical Terms:

1255324
Algebraic geometry.

LC Class. No.: QA564-609

Dewey Class. No.: 516.35

Singularities of Mappings = The Local Behaviour of Smooth and Complex Analytic Mappings /
LDR:03448nam a22004095i 4500 001 1018759
003 DE-He213
005 20200703071906.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030344405 $9 978-3-030-34440-5
024 7 $a 10.1007/978-3-030-34440-5 $2 doi
035 $a 978-3-030-34440-5
050 4 $a QA564-609
072 7 $a PBMW $2 bicssc
072 7 $a MAT012010 $2 bisacsh
072 7 $a PBMW $2 thema
082 0 4 $a 516.35 $2 23
100 1 $a Mond, David. $e editor. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1287821
245 1 0 $a Singularities of Mappings $h [electronic resource] : $b The Local Behaviour of Smooth and Complex Analytic Mappings / $c by David Mond, Juan J. Nuño-Ballesteros.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a XV, 567 p. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, $x 0072-7830 ; $v 357
505 0 $a Introduction -- Part I Thom-Mather Theory: Right-Left Equivalence, Stability,Versal Unfoldings, Finite Determinacy -- Manifolds and Smooth Mappings -- Left-Right Equivalence and Stability -- Contact Equivalence -- Versal Unfoldings -- Finite Determinacy -- Classification of Stable Germs by Their Local Algebras -- Part II Images and Discriminants: The Topology of Stable Perturbations -- Stable Images and Discriminants -- Multiple Points -- Calculating the Homology of the Image -- Multiple Points in the Target: The Case of Parameterised Hypersurfaces -- Appendix A: Jet Spaces and Jet Bundles -- Appendix B Stratifications -- Appendix C Background in Commutative Algebra -- Appendix D Local Analytic Geometry -- Appendix E Sheaves. References -- Index.
520 $a The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings. Part I of the book develops the now classical real C∞ and complex analytic theories jointly. Standard topics such as stability, deformation theory and finite determinacy, are covered in this part. In Part II of the book, the authors focus on the complex case. The treatment is centred around the idea of the "nearby stable object" associated to an unstable map-germ, which includes in particular the images and discriminants of stable perturbations of unstable singularities. This part includes recent research results, bringing the reader up to date on the topic. By focusing on singularities of mappings, rather than spaces, this book provides a necessary addition to the literature. Many examples and exercises, as well as appendices on background material, make it an invaluable guide for graduate students and a key reference for researchers. A number of graduate level courses on singularities of mappings could be based on the material it contains.
650 0 $a Algebraic geometry. $3 1255324
650 0 $a Functions of complex variables. $3 528649
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Complex manifolds. $3 676705
650 1 4 $a Algebraic Geometry. $3 670184
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 672032
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology). $3 668590
700 1 $a Nuño-Ballesteros, Juan J. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1313847
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030344399
776 0 8 $i Printed edition: $z 9783030344412
776 0 8 $i Printed edition: $z 9783030344429
830 0 $a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, $x 0072-7830 ; $v 351 $3 1257746
856 4 0 $u https://doi.org/10.1007/978-3-030-34440-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)