Lectures on K3 surfaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, United Kingdom
Cambridge University Press
2016
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| Series: | Cambridge studies in advanced mathematics
158 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 485 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107153042 |
Staff View
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Record in the Search Index
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| adam_text | Contents Preface Definitions Algebraic КЗ Surfaces Classical Invariants Complex КЗ Surfaces More Examples page ix 1 Basic 1 2 3 4 2 Linear Systems 1 General Results: Linear Sv stems. Curves.Vanishing 2 Smooth Curves on КЗ Surfaces 3 Vanishing and Global Generation 4 Existence of КЗ Surfaces 16 16 21 24 31 3 Hodge Structures 1 Abstract Notions 2 Geometry of Hodge Structures of WeightOne and Two 3 Endomorphism Fields and Mumford-Tate Groups 35 35 42 49 4 Kuga-Satake Construction 1 Clifford Algebra anil Spin-Group 2 From Weight Two to Weight One 3 Kuga-Satake Varieties of Special Surfaces 4 Appendix: Weil Conjectures 59 59 62 70 73 5 Moduli Spaces of Polarized КЗ Surfaces 1 Moduli Functor 2 Via Hilbert Schemes 3 Local Structure 4 As Delisme-Mumford Stack 81 81 85 91 94 1 1 4 8 13
Contents vi 6 7 8 Periods 1 Period Domains 2 Local Period Map and Noether-Lefscheiz Locus 3 Global Period Map 4 Moduli Spaces of КЗ Surfaces via Periods andApplications 5 Appendix: Kulikov Models KK) HK) Surjectivity of the Period Map and Global Torelli 1 Deformation Equivalence of КЗ Surfaces 2 Moduli Space of Marked КЗ Surfaces 3 Twistor Lines 4 Local and Global Surjectivity of the Period Map 5 Global Torelli Theorem 6 Other Approaches 12X Ample Cone and Kähler Cone 1 Ample and Nef Cone 2 Chambers and Walls 3 Effective Cone 4 Cone Conjecture 5 Kähler Cone 105 112 I 17 124 12X 131 133 138 13P 145 14 S 14S 152 Ի՛7 I (՝5 170 Vector Bundles on КЗ Surfaces 1 Basic Techniques and First Examples 2 Simple Vector Bundles and Brill-Noether General Curves 3 Stability of Special Bundles 4 Stability of the Tangent Bundle 5 Appendix: Lifting КЗ Surfaces I ՜5 I 5 I SO 10 Moduli Spaces of Sheaves on КЗ Surfaces 1 General Theory 2 On КЗ Surfaces 3 Some Moduli Spaces 1լ)օ loo 205 21 ! 11 Elliptic КЗ Surfaces 1 Singular Fibres 2 Weierstrass Equation 3 Mordell-Weil Group 4 Jacobian Fibration 5 Tate-Safarevič Group 2 Iо 21 о 22(՝ 232 238 244 12 Chow Ring and Grothendieck Group 1 General Facts on CH* (X) and K(X) 254 254 9 184 1S՜1 Iо ՝
Contents vii Chow Groups: Mumford and Bloch-Beïlinson Beauville-Voisin Ring 259 267 13 Rational Curves on КЗ Surfaces 1 Existence Results 2 Deformation Theory and Families of Elliptic Curves 3 Arithmetic Aspects 4 Counting of Rational Curves 5 Density Results 272 276 282 288 293 295 14 Lattices 1 Existence, Uniqueness, and Embeddings of Lattices 2 Orthogonal Group 3 Embeddings of Picard, Transcendental, and Kummer Lattices 4 Niemeier Lattices 299 305 311 314 324 15 Automorphisms 1 Symplectic Automorphisms 2 Automorphisms via Periods 3 Finite Groups of Symplectic Automorphisms 4 Nikulin Involutions, Shioda-Inose Structures, and More 330 330 337 344 352 16 Derived Categories 1 Derived Categories and Fourier-Mukai Transforms 2 Examples of (Auto)equivalences 3 Action on Cohomology 4 Twisted, Non-projective, and in Positive Characteristic 5 Appendix: Twisted КЗ Surfaces 358 358 364 369 376 382 17 Picard Group 1 Picard Groups of Complex КЗ Surfaces 2 Algebraic Aspects 3 Tate Conjecture 385 385 391 403 18 Brauer Group I General Theory: Arithmetic, Geometric, Formal 2 Finiteness of Brauer Group 3 Height 410 410 420 427 2 3 References Index List of Notation 438 472 483
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:39:31Z |
| institution | BVB |
| isbn | 9781107153042 |
| language | English |
| lccn | 016019204 |
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| physical | xi, 485 Seiten Illustrationen, Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Huybrechts, Daniel 1966- Verfasser (DE-588)113483716 aut Lectures on K3 surfaces Daniel Huybrechts (University of Bonn) Cambridge, United Kingdom Cambridge University Press 2016 xi, 485 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 158 Surfaces, Algebraic Threefolds (Algebraic geometry) Geometry, Algebraic Cambridge studies in advanced mathematics 158 (DE-604)BV000003678 158 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029358707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Huybrechts, Daniel 1966- Lectures on K3 surfaces Cambridge studies in advanced mathematics Surfaces, Algebraic Threefolds (Algebraic geometry) Geometry, Algebraic |
| title | Lectures on K3 surfaces |
| title_auth | Lectures on K3 surfaces |
| title_exact_search | Lectures on K3 surfaces |
| title_full | Lectures on K3 surfaces Daniel Huybrechts (University of Bonn) |
| title_fullStr | Lectures on K3 surfaces Daniel Huybrechts (University of Bonn) |
| title_full_unstemmed | Lectures on K3 surfaces Daniel Huybrechts (University of Bonn) |
| title_short | Lectures on K3 surfaces |
| title_sort | lectures on k3 surfaces |
| topic | Surfaces, Algebraic Threefolds (Algebraic geometry) Geometry, Algebraic |
| topic_facet | Surfaces, Algebraic Threefolds (Algebraic geometry) Geometry, Algebraic |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029358707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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