Introduction to Toric varieties:
Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Ri...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
[1993]
|
| Series: | Annals of Mathematics Studies
number 131 |
| Subjects: | |
| Online Access: | Volltext |
| Summary: | Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry |
| Item Description: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Physical Description: | 1 online resource |
| ISBN: | 9781400882526 |
| DOI: | 10.1515/9781400882526 |
Staff View
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| 520 | |a Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry | ||
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Record in the Search Index
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| author | Fulton, William 1939- |
| author_GND | (DE-588)136272541 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/53 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400882526 |
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| id | DE-604.BV043712512 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:33:08Z |
| institution | BVB |
| isbn | 9781400882526 |
| language | English |
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| publishDate | 1993 |
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| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Fulton, William 1939- (DE-588)136272541 aut Introduction to Toric varieties William Fulton Princeton, NJ Princeton University Press [1993] © 1993 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 131 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) Toric varieties are algebraic varieties arising from elementary geometric and combinatorial objects such as convex polytopes in Euclidean space with vertices on lattice points. Since many algebraic geometry notions such as singularities, birational maps, cycles, homology, intersection theory, and Riemann-Roch translate into simple facts about polytopes, toric varieties provide a marvelous source of examples in algebraic geometry. In the other direction, general facts from algebraic geometry have implications for such polytopes, such as to the problem of the number of lattice points they contain. In spite of the fact that toric varieties are very special in the spectrum of all algebraic varieties, they provide a remarkably useful testing ground for general theories. The aim of this mini-course is to develop the foundations of the study of toric varieties, with examples, and describe some of these relations and applications. The text concludes with Stanley's theorem characterizing the numbers of simplicies in each dimension in a convex simplicial polytope. Although some general theorems are quoted without proof, the concrete interpretations via simplicial geometry should make the text accessible to beginners in algebraic geometry In English Toric varieties Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Torische Varietät (DE-588)4786945-8 gnd rswk-swf Toruseinbettung (DE-588)4194508-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Mannigfaltigkeit (DE-588)4037379-4 s 1\p DE-604 Toruseinbettung (DE-588)4194508-6 s 2\p DE-604 Torische Varietät (DE-588)4786945-8 s 3\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-03332-3 Annals of Mathematics Studies number 131 (DE-604)BV040389493 131 https://doi.org/10.1515/9781400882526?locatt=mode:legacy Verlag URL des Erstveröffentlichers 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Fulton, William 1939- Introduction to Toric varieties Annals of Mathematics Studies Toric varieties Algebraische Geometrie (DE-588)4001161-6 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Torische Varietät (DE-588)4786945-8 gnd Toruseinbettung (DE-588)4194508-6 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4037379-4 (DE-588)4786945-8 (DE-588)4194508-6 |
| title | Introduction to Toric varieties |
| title_auth | Introduction to Toric varieties |
| title_exact_search | Introduction to Toric varieties |
| title_full | Introduction to Toric varieties William Fulton |
| title_fullStr | Introduction to Toric varieties William Fulton |
| title_full_unstemmed | Introduction to Toric varieties William Fulton |
| title_short | Introduction to Toric varieties |
| title_sort | introduction to toric varieties |
| topic | Toric varieties Algebraische Geometrie (DE-588)4001161-6 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Torische Varietät (DE-588)4786945-8 gnd Toruseinbettung (DE-588)4194508-6 gnd |
| topic_facet | Toric varieties Algebraische Geometrie Mannigfaltigkeit Torische Varietät Toruseinbettung |
| url | https://doi.org/10.1515/9781400882526?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT fultonwilliam introductiontotoricvarieties |