Lectures on Hilbert schemes of points on surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1999]
|
| Series: | University lecture series
Volume 18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 132 Seiten Illustrationen, Diagramme |
| ISBN: | 0821819569 9780821819562 |
Staff View
MARC
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| 245 | 1 | 0 | |a Lectures on Hilbert schemes of points on surfaces |c Hiraku Nakajima |
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| 264 | 4 | |c © 1999 | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Introduction 1
Chapter 1. Hilbert scheme of points 5
1.1. General Results on the Hilbert scheme 5
1.2. Hilbert scheme of points on the plane 7
1.3. Hilbert scheme of points on a surface 12
1.4. Symplectic structure 13
1.5. The Douady space 15
Chapter 2. Framed moduli space of torsion free sheaves on P2 17
2.1. Monad 18
2.2. Rank 1 case 24
Chapter 3. Hyper Kahler metric on (C2)1 1 29
3.1. Geometric invariant theory and the moment map 29
3.2. Hyper Kahler quotients 37
Chapter 4. Resolution of simple singularities 47
4.1. General Statement 47
4.2. Dynkin diagrams 49
4.3. A geometric realization of the McKay correspondence 52
Chapter 5. Poincare polynomials of the Hilbert schemes (1) 59
5.1. Perfectness of the Morse function arising from the moment map 59
5.2. Poincare polynomial of (C2)W 63
Chapter 6. Poincare polynomials of Hilbert schemes (2) 73
6.1. Results on intersection cohomology 73
6.2. Proof of the formula 75
Chapter 7. Hilbert scheme on the cotangent bundle of a Riemann surface 79
7.1. Morse theory on holomorphic symplectic manifolds 79
7.2. Hilbert scheme of T*E 80
7.3. Analogy with the moduli space of Higgs bundles 85
Chapter 8. Homology group of the Hilbert schemes and the Heisenberg algebra 89
8.1. Heisenberg algebra and Clifford algebra 89
8.2. Correspondences 91
8.3. Main construction 93
8.4. Proof of Theorem 8.13 96
vii
viii CONTENTS
Chapter 9. Symmetric products of an embedded curve, symmetric functions
and vertex operators 105
9.1. Symmetric functions and symmetric groups 105
9.2. Grojnowski s formulation 109
9.3. Symmetric products of an embedded curve 110
9.4. Vertex algebra 114
9.5. Moduli space of rank 1 sheaves 121
Bibliography 125
Index 131
|
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| author | Nakajima, Hiraku 1962- |
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| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012870536 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:12Z |
| institution | BVB |
| isbn | 0821819569 9780821819562 |
| language | English |
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| physical | xi, 132 Seiten Illustrationen, Diagramme |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | University lecture series |
| series2 | University lecture series |
| spelling | Nakajima, Hiraku 1962- Verfasser (DE-588)173515835 aut Lectures on Hilbert schemes of points on surfaces Hiraku Nakajima Providence, Rhode Island American Mathematical Society [1999] © 1999 xi, 132 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier University lecture series Volume 18 Algebraische Fläche (DE-588)4195660-6 gnd rswk-swf Hilbertsches Schema (DE-588)4159868-4 gnd rswk-swf Hilbertsches Schema (DE-588)4159868-4 s Algebraische Fläche (DE-588)4195660-6 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1834-2 University lecture series Volume 18 (DE-604)BV004153846 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008759503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nakajima, Hiraku 1962- Lectures on Hilbert schemes of points on surfaces University lecture series Algebraische Fläche (DE-588)4195660-6 gnd Hilbertsches Schema (DE-588)4159868-4 gnd |
| subject_GND | (DE-588)4195660-6 (DE-588)4159868-4 |
| title | Lectures on Hilbert schemes of points on surfaces |
| title_auth | Lectures on Hilbert schemes of points on surfaces |
| title_exact_search | Lectures on Hilbert schemes of points on surfaces |
| title_full | Lectures on Hilbert schemes of points on surfaces Hiraku Nakajima |
| title_fullStr | Lectures on Hilbert schemes of points on surfaces Hiraku Nakajima |
| title_full_unstemmed | Lectures on Hilbert schemes of points on surfaces Hiraku Nakajima |
| title_short | Lectures on Hilbert schemes of points on surfaces |
| title_sort | lectures on hilbert schemes of points on surfaces |
| topic | Algebraische Fläche (DE-588)4195660-6 gnd Hilbertsches Schema (DE-588)4159868-4 gnd |
| topic_facet | Algebraische Fläche Hilbertsches Schema |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008759503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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