Hyperplane arrangements: an introduction
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2017]
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| Series: | Universitext
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 200 Seiten Illustrationen, Diagramme (teilweise farbig) |
| ISBN: | 9783319562209 |
| ISSN: | 0172-5939 |
Staff View
MARC
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| 100 | 1 | |a Dimca, Alexandru |d 1953- |0 (DE-588)1241582173 |4 aut | |
| 245 | 1 | 0 | |a Hyperplane arrangements |b an introduction |c Alexandru Dimca |
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| 650 | 4 | |a Commutative algebra | |
| 650 | 4 | |a Commutative rings | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Algorithms | |
| 650 | 4 | |a Projective geometry | |
| 650 | 4 | |a Combinatorics | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Commutative Rings and Algebras | |
| 650 | 4 | |a Several Complex Variables and Analytic Spaces | |
| 650 | 4 | |a Projective Geometry | |
| 650 | 4 | |a Mathematik | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Invitation to the Trip...................................... . . . . 1
1.1 Linear Partitions and the Topology of Complements........... 1
1.2 Finite Fields and Cohomology............................ 9
1.3 Exercises................................................... 13
2 Hyperplane Arrangements and Their Combinatorics.............. 15
2.1 Central, Affine and Projective Arrangements................. 15
2.2 The Intersection Lattice and the Möbius Function ........... 21
2.3 Deletion-Restriction Theorems and the Number of Regions..... 31
2.4 Graphic Arrangements and Reflection Arrangements.............. 37
2.5 Exercises................................................... 40
3 Orlik-Solomon Algebras and de Rham Cohomology.................... 45
3.1 Orlik-Solomon Algebras for Hyperplane Arrangements............ 45
3.2 The Amold-Brieskom and Orlik-Solomon Theorems................. 53
3.3 Exercises..................................................... 59
4 On the Topology of the Complement M(s/).......................... 61
4.1 Complements of Projective Hypersurfaces....................... 61
4.2 Minimality of M{s?) and the Degree of the Gradient Map...... 66
4.3 The Fundamental Group of the Complement 71
4.4 Exercises .................................................... 82
5 Milnor Fibers and Local Systems.................................. 85
5.1 Milnor Fibers and Monodromy............................... 85
5.2 Monodromy Eigenspaces and Twisted Cohomology ................. 90
5.3 Exercises..................................................... 97
6 Characteristic Varieties and Resonance Varieties................. 99
6.1 Topological and Algebraic Jumping Loci........................ 99
6.2 Jumping Loci and Pencils of Plane Curves . .................. 108
6.3 Translated Components in the Characteristic Varieties........ 114
XI
xii Contents
6.4 The Deleted £3-Line Airangement................................. 118
6.5 Exercises....................................................... 122
7 Logarithmic Connections and Mixed Hodge Structures . ................ 125
7.1 Two Theorems of Pierre Deligne.................................. 125
7.2 Mixed Hodge Structure and Spectrum.............................. 135
7.3 Polynomial Count Varieties...................................... 140
7.4 Exercises....................................................... 147
8 Free Arrangements and de Rham Cohomology
of Mhnor Fibers...................................................... 151
8.1 Free Divisors and Logarithmic Differential Forms................ 151
8.2 Free Curves, Free Line Arrangements, and Terao’s Conjecture . .. 159
8.3 Spectral Sequences and Alexander Polynomials................... 168
8.4 The de Rham Cohomology of Milnor Fibers......................... 178
8.5 Exercises....................................................... 184
References.............................................................. 187
Index................................................................... 197
|
| any_adam_object | 1 |
| author | Dimca, Alexandru 1953- |
| author_GND | (DE-588)1241582173 |
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| author_sort | Dimca, Alexandru 1953- |
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| bvnumber | BV044704834 |
| classification_rvk | SK 300 SK 380 |
| ctrlnum | (OCoLC)988839907 (DE-599)BVBBV044704834 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:59:51Z |
| institution | BVB |
| isbn | 9783319562209 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030101485 |
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| owner_facet | DE-355 DE-BY-UBR DE-11 DE-83 DE-188 |
| physical | xii, 200 Seiten Illustrationen, Diagramme (teilweise farbig) |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Dimca, Alexandru 1953- (DE-588)1241582173 aut Hyperplane arrangements an introduction Alexandru Dimca Cham Springer [2017] © 2017 xii, 200 Seiten Illustrationen, Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier Universitext 0172-5939 Mathematics Algebraic geometry Commutative algebra Commutative rings Functions of complex variables Algorithms Projective geometry Combinatorics Algebraic Geometry Commutative Rings and Algebras Several Complex Variables and Analytic Spaces Projective Geometry Mathematik Erscheint auch als Online-Ausgabe 10.1007/978-3-319-56221-6 Erscheint auch als Online-Ausgabe 978-3-319-56221-6 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=030101485&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dimca, Alexandru 1953- Hyperplane arrangements an introduction Mathematics Algebraic geometry Commutative algebra Commutative rings Functions of complex variables Algorithms Projective geometry Combinatorics Algebraic Geometry Commutative Rings and Algebras Several Complex Variables and Analytic Spaces Projective Geometry Mathematik |
| title | Hyperplane arrangements an introduction |
| title_auth | Hyperplane arrangements an introduction |
| title_exact_search | Hyperplane arrangements an introduction |
| title_full | Hyperplane arrangements an introduction Alexandru Dimca |
| title_fullStr | Hyperplane arrangements an introduction Alexandru Dimca |
| title_full_unstemmed | Hyperplane arrangements an introduction Alexandru Dimca |
| title_short | Hyperplane arrangements |
| title_sort | hyperplane arrangements an introduction |
| title_sub | an introduction |
| topic | Mathematics Algebraic geometry Commutative algebra Commutative rings Functions of complex variables Algorithms Projective geometry Combinatorics Algebraic Geometry Commutative Rings and Algebras Several Complex Variables and Analytic Spaces Projective Geometry Mathematik |
| topic_facet | Mathematics Algebraic geometry Commutative algebra Commutative rings Functions of complex variables Algorithms Projective geometry Combinatorics Algebraic Geometry Commutative Rings and Algebras Several Complex Variables and Analytic Spaces Projective Geometry Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030101485&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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