Introduction to tropical geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2015]
|
| Schriftenreihe: | Graduate studies in mathematics
161 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xii, 363 Seiten Diagramme |
| ISBN: | 9780821851982 |
Internformat
MARC
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| 100 | 1 | |a Maclagan, Diane |d 1974- |0 (DE-588)1071745972 |4 aut | |
| 245 | 1 | 0 | |a Introduction to tropical geometry |c Diane Maclagan, Bernd Sturmfels |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2015] | |
| 264 | 4 | |c © 2015 | |
| 300 | |a xii, 363 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 161 | |
| 650 | 7 | |a Algebraic geometry ... Tropical geometry ... Tropical geometry |2 msc | |
| 650 | 7 | |a Combinatorics ... Designs and configurations ... Matroids, geometric lattices |2 msc | |
| 650 | 7 | |a Field theory and polynomials ... Topological fields ... Non-Archimedean valued fields |2 msc | |
| 650 | 7 | |a Commutative algebra ... Computational aspects and applications ... Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) |2 msc | |
| 650 | 7 | |a Algebraic geometry ... Special varieties ... Toric varieties, Newton polyhedra |2 msc | |
| 650 | 7 | |a Linear and multilinear algebra; matrix theory ... Basic linear algebra ... Max-plus and related algebras |2 msc | |
| 650 | 7 | |a Convex and discrete geometry ... Polytopes and polyhedra ... Lattice polytopes (including relations with commutative algebra and algebraic geometry) |2 msc | |
| 650 | 4 | |a Tropical geometry |x Study and teaching (Graduate) | |
| 650 | 4 | |a Geometry, Algebraic |x Study and teaching (Graduate) | |
| 650 | 0 | 7 | |a Tropische Geometrie |0 (DE-588)7566380-6 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Sturmfels, Bernd |d 1962- |0 (DE-588)121330435 |4 aut | |
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| 830 | 0 | |a Graduate studies in mathematics |v 161 |w (DE-604)BV009739289 |9 161 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027768166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027768166 | ||
Datensatz im Suchindex
| _version_ | 1804152936827191296 |
|---|---|
| adam_text | Contents
Preface
ix
Chapter
1.
Tropical Islands
1
§1.1.
Arithmetic
2
§1.2.
Dynamic Programming
7
§1.3.
Plane Curves
11
§1.4.
Amoebas and their Tentacles
17
§1.5.
Implicitization
21
§1.6.
Group Theory
25
§1.7.
Curve Counting
31
§1.8.
Compactifications
34
§1.9.
Exercises
39
Chapter
2.
Building Blocks
43
§2.1.
Fields
43
§2.2.
Algebraic Varieties
52
§2.3.
Polyhedral Geometry
58
§2.4. Gröbner
Bases
65
§2.5. Gröbner
Complexes
74
§2.6.
Tropical Bases
81
§2.7.
Exercises
89
Chapter
3.
Tropical Varieties
93
§3.1.
Hypersurfaces
93
vii
viii Contents
§3.2.
The Fundamental Theorem
102
§3.3.
The Structure Theorem
110
§3.4.
Multiplicities and Balancing
118
§3.5.
Connectivity and Fans
128
§3.6.
Stable Intersection
133
§3.7.
Exercises
149
Chapter
4.
Tropical Rain Forest
153
§4.1. Hyperplane
Arrangements
153
§4.2.
Matroids
161
§4.3.
Grassmannians
170
§4.4.
Linear Spaces
182
§4.5.
Surfaces
192
§4.6.
Complete Intersections
201
§4.7.
Exercises
214
Chapter
5.
Tropical Garden
221
§5.1.
Eigenvalues and Eigenvectors
222
§5.2.
Tropical Convexity
228
§5.3.
The Rank of a Matrix
243
§5.4.
Arrangements of Trees
255
§5.5.
Monomials in Linear Forms
268
§5.6.
Exercises
273
Chapter
6.
Toric Connections
277
§6.1.
Toric Background
278
§6.2.
Tropicalizing Toric Varieties
281
§6.3.
Orbits
291
§6.4.
Tropical Compactifications
297
§6.5.
Geometric Tropicalization
309
§6.6.
Degenerations
322
§6.7.
Intersection Theory
334
§6.8.
Exercises
346
Bibliography
351
Index
361
|
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| indexdate | 2024-07-10T01:18:38Z |
| institution | BVB |
| isbn | 9780821851982 |
| language | English |
| lccn | 014036141 |
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| spelling | Maclagan, Diane 1974- (DE-588)1071745972 aut Introduction to tropical geometry Diane Maclagan, Bernd Sturmfels Providence, Rhode Island American Mathematical Society [2015] © 2015 xii, 363 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 161 Algebraic geometry ... Tropical geometry ... Tropical geometry msc Combinatorics ... Designs and configurations ... Matroids, geometric lattices msc Field theory and polynomials ... Topological fields ... Non-Archimedean valued fields msc Commutative algebra ... Computational aspects and applications ... Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) msc Algebraic geometry ... Special varieties ... Toric varieties, Newton polyhedra msc Linear and multilinear algebra; matrix theory ... Basic linear algebra ... Max-plus and related algebras msc Convex and discrete geometry ... Polytopes and polyhedra ... Lattice polytopes (including relations with commutative algebra and algebraic geometry) msc Tropical geometry Study and teaching (Graduate) Geometry, Algebraic Study and teaching (Graduate) Tropische Geometrie (DE-588)7566380-6 gnd rswk-swf Tropische Geometrie (DE-588)7566380-6 s DE-604 Sturmfels, Bernd 1962- (DE-588)121330435 aut Erscheint auch als Online-Ausgabe 978-1-4704-2221-9 Graduate studies in mathematics 161 (DE-604)BV009739289 161 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=027768166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Maclagan, Diane 1974- Sturmfels, Bernd 1962- Introduction to tropical geometry Graduate studies in mathematics Algebraic geometry ... Tropical geometry ... Tropical geometry msc Combinatorics ... Designs and configurations ... Matroids, geometric lattices msc Field theory and polynomials ... Topological fields ... Non-Archimedean valued fields msc Commutative algebra ... Computational aspects and applications ... Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) msc Algebraic geometry ... Special varieties ... Toric varieties, Newton polyhedra msc Linear and multilinear algebra; matrix theory ... Basic linear algebra ... Max-plus and related algebras msc Convex and discrete geometry ... Polytopes and polyhedra ... Lattice polytopes (including relations with commutative algebra and algebraic geometry) msc Tropical geometry Study and teaching (Graduate) Geometry, Algebraic Study and teaching (Graduate) Tropische Geometrie (DE-588)7566380-6 gnd |
| subject_GND | (DE-588)7566380-6 |
| title | Introduction to tropical geometry |
| title_auth | Introduction to tropical geometry |
| title_exact_search | Introduction to tropical geometry |
| title_full | Introduction to tropical geometry Diane Maclagan, Bernd Sturmfels |
| title_fullStr | Introduction to tropical geometry Diane Maclagan, Bernd Sturmfels |
| title_full_unstemmed | Introduction to tropical geometry Diane Maclagan, Bernd Sturmfels |
| title_short | Introduction to tropical geometry |
| title_sort | introduction to tropical geometry |
| topic | Algebraic geometry ... Tropical geometry ... Tropical geometry msc Combinatorics ... Designs and configurations ... Matroids, geometric lattices msc Field theory and polynomials ... Topological fields ... Non-Archimedean valued fields msc Commutative algebra ... Computational aspects and applications ... Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) msc Algebraic geometry ... Special varieties ... Toric varieties, Newton polyhedra msc Linear and multilinear algebra; matrix theory ... Basic linear algebra ... Max-plus and related algebras msc Convex and discrete geometry ... Polytopes and polyhedra ... Lattice polytopes (including relations with commutative algebra and algebraic geometry) msc Tropical geometry Study and teaching (Graduate) Geometry, Algebraic Study and teaching (Graduate) Tropische Geometrie (DE-588)7566380-6 gnd |
| topic_facet | Algebraic geometry ... Tropical geometry ... Tropical geometry Combinatorics ... Designs and configurations ... Matroids, geometric lattices Field theory and polynomials ... Topological fields ... Non-Archimedean valued fields Commutative algebra ... Computational aspects and applications ... Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) Algebraic geometry ... Special varieties ... Toric varieties, Newton polyhedra Linear and multilinear algebra; matrix theory ... Basic linear algebra ... Max-plus and related algebras Convex and discrete geometry ... Polytopes and polyhedra ... Lattice polytopes (including relations with commutative algebra and algebraic geometry) Tropical geometry Study and teaching (Graduate) Geometry, Algebraic Study and teaching (Graduate) Tropische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027768166&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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