國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Singularities of mappingsthe local b...

Mond, David.

Singularities of mappingsthe local behaviour of smooth and complex analytic mappings /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Singularities of mappingsby David Mond, Juan J. Nuno-Ballesteros.
其他題名:	the local behaviour of smooth and complex analytic mappings /
作者:	Mond, David.
其他作者:	Nuno-Ballesteros, Juan J.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	xv, 567 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Singularities (Mathematics)
電子資源:	https://doi.org/10.1007/978-3-030-34440-5
ISBN:	9783030344405$q(electronic bk.)

Singularities of mappingsthe 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. Nuno-Ballesteros. - Cham :Springer International Publishing :2020. - xv, 567 p. :ill., digital ;24 cm. - Grundlehren der mathematischen wissenschaften,v.3570072-7830 ;. - Grundlehren der mathematischen wissenschaften ;342..

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$q(electronic bk.)

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

185806
Singularities (Mathematics)

LC Class. No.: QA614.58 / .M663 2020

Dewey Class. No.: 516.35

Singularities of mappingsthe local behaviour of smooth and complex analytic mappings /
LDR:03041nmm a2200337 a 4500 001 573677
003 DE-He213
005 20200624145347.0
006 m d
007 cr nn 008maaau
008 200928s2020 sz s 0 eng d
020 $a 9783030344405$q(electronic bk.)
020 $a 9783030344399$q(paper)
024 7 $a 10.1007/978-3-030-34440-5 $2 doi
035 $a 978-3-030-34440-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA614.58 $b .M663 2020
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
090 $a QA614.58 $b .M741 2020
100 1 $a Mond, David. $3 861038
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. Nuno-Ballesteros.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2020.
300 $a xv, 567 p. : $b ill., digital ; $c 24 cm.
490 1 $a Grundlehren der mathematischen wissenschaften, $x 0072-7830 ; $v 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 Singularities (Mathematics) $3 185806
650 0 $a Mappings (Mathematics) $3 338109
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 276692
650 2 4 $a Manifolds and Cell Complexes (incl. Diff.Topology) $3 253172
700 1 $a Nuno-Ballesteros, Juan J. $3 861039
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Grundlehren der mathematischen wissenschaften ; $v 342. $3 597051
856 4 0 $u https://doi.org/10.1007/978-3-030-34440-5
950 $a Mathematics and Statistics (Springer-11649)