國立高雄大學圖資館 |

Language: English

Back

Intersection homology & perverse she...

Maxim, Laurentiu G.

Intersection homology & perverse sheaveswith applications to singularities /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Intersection homology & perverse sheavesby Laurentiu G. Maxim.
Reminder of title:	with applications to singularities /
Author:	Maxim, Laurentiu G.
Published:	Cham :Springer International Publishing :2019.
Description:	xv, 270 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Intersection homology theory.
Online resource:	https://doi.org/10.1007/978-3-030-27644-7
ISBN:	9783030276447$q(electronic bk.)

Intersection homology & perverse sheaveswith applications to singularities /
Maxim, Laurentiu G.

Intersection homology & perverse sheaveswith applications to singularities /[electronic resource] :by Laurentiu G. Maxim. - Cham :Springer International Publishing :2019. - xv, 270 p. :ill., digital ;24 cm. - Graduate texts in mathematics,2810072-5285 ;. - Graduate texts in mathematics ;129..

Preface -- 1. Topology of singular spaces: motivation, overview -- 2. Intersection Homology: definition, properties -- 3. L-classes of stratified spaces -- 4. Brief introduction to sheaf theory -- 5. Poincare-Verdier Duality -- 6. Intersection homology after Deligne -- 7. Constructibility in algebraic geometry -- 8. Perverse sheaves -- 9. The Decomposition Package and Applications -- 10. Hypersurface singularities. Nearby and vanishing cycles -- 11. Overview of Saito's mixed Hodge modules, and immediate applications -- 12. Epilogue -- Bibliography -- Index.

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson-Bernstein-Deligne-Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito's deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.

ISBN: 9783030276447$q(electronic bk.)

Standard No.: 10.1007/978-3-030-27644-7doiSubjects--Topical Terms:

470574
Intersection homology theory.

LC Class. No.: QA612.32 / .M38 2019

Dewey Class. No.: 514.23

Intersection homology & perverse sheaveswith applications to singularities /
LDR:03213nmm a2200337 a 4500 001 569677
003 DE-He213
005 20191130212406.0
006 m d
007 cr nn 008maaau
008 200723s2019 gw s 0 eng d
020 $a 9783030276447$q(electronic bk.)
020 $a 9783030276430$q(paper)
024 7 $a 10.1007/978-3-030-27644-7 $2 doi
035 $a 978-3-030-27644-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA612.32 $b .M38 2019
072 7 $a PBPD $2 bicssc
072 7 $a MAT038000 $2 bisacsh
072 7 $a PBPD $2 thema
082 0 4 $a 514.23 $2 23
090 $a QA612.32 $b .M464 2019
100 1 $a Maxim, Laurentiu G. $3 855781
245 1 0 $a Intersection homology & perverse sheaves $h [electronic resource] : $b with applications to singularities / $c by Laurentiu G. Maxim.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xv, 270 p. : $b ill., digital ; $c 24 cm.
490 1 $a Graduate texts in mathematics, $x 0072-5285 ; $v 281
505 0 $a Preface -- 1. Topology of singular spaces: motivation, overview -- 2. Intersection Homology: definition, properties -- 3. L-classes of stratified spaces -- 4. Brief introduction to sheaf theory -- 5. Poincare-Verdier Duality -- 6. Intersection homology after Deligne -- 7. Constructibility in algebraic geometry -- 8. Perverse sheaves -- 9. The Decomposition Package and Applications -- 10. Hypersurface singularities. Nearby and vanishing cycles -- 11. Overview of Saito's mixed Hodge modules, and immediate applications -- 12. Epilogue -- Bibliography -- Index.
520 $a This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout. By giving a taste of the main ideas in the field, the author welcomes new readers to this exciting area at the crossroads of topology, algebraic geometry, analysis, and differential equations. Those looking to delve further into the abstract theory will find ample references to facilitate navigation of both classic and recent literature. Beginning with an introduction to intersection homology from a geometric and topological viewpoint, the text goes on to develop the sheaf-theoretical perspective. Then algebraic geometry comes to the fore: a brief discussion of constructibility opens onto an in-depth exploration of perverse sheaves. Highlights from the following chapters include a detailed account of the proof of the Beilinson-Bernstein-Deligne-Gabber (BBDG) decomposition theorem, applications of perverse sheaves to hypersurface singularities, and a discussion of Hodge-theoretic aspects of intersection homology via Saito's deep theory of mixed Hodge modules. An epilogue offers a succinct summary of the literature surrounding some recent applications. Intersection Homology & Perverse Sheaves is suitable for graduate students with a basic background in topology and algebraic geometry. By building context and familiarity with examples, the text offers an ideal starting point for those entering the field. This classroom-tested approach opens the door to further study and to current research.
650 0 $a Intersection homology theory. $3 470574
650 0 $a Sheaf theory. $3 208695
650 1 4 $a Algebraic Topology. $3 273784
650 2 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Several Complex Variables and Analytic Spaces. $3 276692
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Graduate texts in mathematics ; $v 129. $3 436082
856 4 0 $u https://doi.org/10.1007/978-3-030-27644-7
950 $a Mathematics and Statistics (Springer-11649)