Cox rings:
Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous present...
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| Main Authors: | , , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2015
|
| Series: | Cambridge studies in advanced mathematics
144 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| Summary: | Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty |
| Physical Description: | 1 online resource (viii, 530 Seiten) |
| ISBN: | 9781139175852 |
| DOI: | 10.1017/CBO9781139175852 |
Staff View
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| 520 | |a Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty | ||
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| author | Arzhantsev, Ivan Derenthal, Ulrich 1978- Hausen, Jürgen Laface, Antonio |
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| dewey-full | 516.3/53 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/53 |
| dewey-search | 516.3/53 |
| dewey-sort | 3516.3 253 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9781139175852 |
| format | Electronic eBook |
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| id | DE-604.BV043940173 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:12Z |
| institution | BVB |
| isbn | 9781139175852 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029349143 |
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| physical | 1 online resource (viii, 530 Seiten) |
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| publishDate | 2015 |
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| publisher | Cambridge University Press |
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| spelling | Arzhantsev, Ivan aut Kolʹt͡sa Koksa Cox rings Ivan Arzhantsev, Moscow State University, Ulrich Derenthal, Leibniz Universität Hannover, Jürgen Hausen, Eberhard Karls Universität Tübingen, Antonio Laface, Universidad de Concepción Cambridge Cambridge University Press 2015 1 online resource (viii, 530 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 144 Cox rings are significant global invariants of algebraic varieties, naturally generalizing homogeneous coordinate rings of projective spaces. This book provides a largely self-contained introduction to Cox rings, with a particular focus on concrete aspects of the theory. Besides the rigorous presentation of the basic concepts, other central topics include the case of finitely generated Cox rings and its relation to toric geometry; various classes of varieties with group actions; the surface case; and applications in arithmetic problems, in particular Manin's conjecture. The introductory chapters require only basic knowledge in algebraic geometry. The more advanced chapters also touch on algebraic groups, surface theory, and arithmetic geometry. Each chapter ends with exercises and problems. These comprise mini-tutorials and examples complementing the text, guided exercises for topics not discussed in the text, and, finally, several open problems of varying difficulty Algebraic varieties Rings (Algebra) Ring Mathematik (DE-588)4128084-2 gnd rswk-swf Ring Mathematik (DE-588)4128084-2 s DE-604 Derenthal, Ulrich 1978- (DE-588)132749351 aut Hausen, Jürgen aut Laface, Antonio aut Erscheint auch als Druck-Ausgabe 978-1-107-02462-5 https://doi.org/10.1017/CBO9781139175852 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Arzhantsev, Ivan Derenthal, Ulrich 1978- Hausen, Jürgen Laface, Antonio Cox rings Algebraic varieties Rings (Algebra) Ring Mathematik (DE-588)4128084-2 gnd |
| subject_GND | (DE-588)4128084-2 |
| title | Cox rings |
| title_alt | Kolʹt͡sa Koksa |
| title_auth | Cox rings |
| title_exact_search | Cox rings |
| title_full | Cox rings Ivan Arzhantsev, Moscow State University, Ulrich Derenthal, Leibniz Universität Hannover, Jürgen Hausen, Eberhard Karls Universität Tübingen, Antonio Laface, Universidad de Concepción |
| title_fullStr | Cox rings Ivan Arzhantsev, Moscow State University, Ulrich Derenthal, Leibniz Universität Hannover, Jürgen Hausen, Eberhard Karls Universität Tübingen, Antonio Laface, Universidad de Concepción |
| title_full_unstemmed | Cox rings Ivan Arzhantsev, Moscow State University, Ulrich Derenthal, Leibniz Universität Hannover, Jürgen Hausen, Eberhard Karls Universität Tübingen, Antonio Laface, Universidad de Concepción |
| title_short | Cox rings |
| title_sort | cox rings |
| topic | Algebraic varieties Rings (Algebra) Ring Mathematik (DE-588)4128084-2 gnd |
| topic_facet | Algebraic varieties Rings (Algebra) Ring Mathematik |
| url | https://doi.org/10.1017/CBO9781139175852 |
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