Combinatorial convexity and algebraic geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1996
|
| Schriftenreihe: | Graduate Texts in Mathematics
168 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts |
| Beschreibung: | 1 Online-Ressource (XIV, 372p. 130 illus) |
| ISBN: | 9781461240440 9781461284765 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-4044-0 |
Internformat
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| 500 | |a The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Ewald, Günter 1929-2015 |
| author_GND | (DE-588)122336224 |
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| author_role | aut |
| author_sort | Ewald, Günter 1929-2015 |
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| bvnumber | BV042420198 |
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| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-4044-0 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461240440 9781461284765 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (XIV, 372p. 130 illus) |
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| publisher | Springer New York |
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| series2 | Graduate Texts in Mathematics |
| spelling | Ewald, Günter 1929-2015 Verfasser (DE-588)122336224 aut Combinatorial convexity and algebraic geometry by Günter Ewald New York, NY Springer New York 1996 1 Online-Ressource (XIV, 372p. 130 illus) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 168 0072-5285 The aim of this book is to provide an introduction for students and nonspecialists to a fascinating relation between combinatorial geometry and algebraic geometry, as it has developed during the last two decades. This relation is known as the theory of toric varieties or sometimes as torus embeddings. Chapters I-IV provide a self-contained introduction to the theory of convex poly topes and polyhedral sets and can be used independently of any applications to algebraic geometry. Chapter V forms a link between the first and second part of the book. Though its material belongs to combinatorial convexity, its definitions and theorems are motivated by toric varieties. Often they simply translate algebraic geometric facts into combinatorial language. Chapters VI-VIII introduce toric va rieties in an elementary way, but one which may not, for specialists, be the most elegant. In considering toric varieties, many of the general notions of algebraic geometry occur and they can be dealt with in a concrete way. Therefore, Part 2 of the book may also serve as an introduction to algebraic geometry and preparation for farther reaching texts about this field. The prerequisites for both parts of the book are standard facts in linear algebra (including some facts on rings and fields) and calculus. Assuming those, all proofs in Chapters I-VII are complete with one exception (IV, Theorem 5.1). In Chapter VIII we use a few additional prerequisites with references from appropriate texts Mathematics Geometry, algebraic Combinatorics Algebraic Geometry Mathematik Torus (DE-588)4185738-0 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Toruseinbettung (DE-588)4194508-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Toruseinbettung (DE-588)4194508-6 s Kombinatorische Geometrie (DE-588)4140733-7 s Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 Torus (DE-588)4185738-0 s 2\p DE-604 https://doi.org/10.1007/978-1-4612-4044-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ewald, Günter 1929-2015 Combinatorial convexity and algebraic geometry Mathematics Geometry, algebraic Combinatorics Algebraic Geometry Mathematik Torus (DE-588)4185738-0 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd Toruseinbettung (DE-588)4194508-6 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4185738-0 (DE-588)4140733-7 (DE-588)4194508-6 (DE-588)4001161-6 |
| title | Combinatorial convexity and algebraic geometry |
| title_auth | Combinatorial convexity and algebraic geometry |
| title_exact_search | Combinatorial convexity and algebraic geometry |
| title_full | Combinatorial convexity and algebraic geometry by Günter Ewald |
| title_fullStr | Combinatorial convexity and algebraic geometry by Günter Ewald |
| title_full_unstemmed | Combinatorial convexity and algebraic geometry by Günter Ewald |
| title_short | Combinatorial convexity and algebraic geometry |
| title_sort | combinatorial convexity and algebraic geometry |
| topic | Mathematics Geometry, algebraic Combinatorics Algebraic Geometry Mathematik Torus (DE-588)4185738-0 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd Toruseinbettung (DE-588)4194508-6 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Combinatorics Algebraic Geometry Mathematik Torus Kombinatorische Geometrie Toruseinbettung Algebraische Geometrie |
| url | https://doi.org/10.1007/978-1-4612-4044-0 |
| work_keys_str_mv | AT ewaldgunter combinatorialconvexityandalgebraicgeometry |