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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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Bibliographische Detailangaben
Hauptverfasser:	Arzhantsev, Ivan (VerfasserIn), Derenthal, Ulrich 1978- (VerfasserIn), Hausen, Jürgen (VerfasserIn), Laface, Antonio (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Cambridge Cambridge University Press 2015
Schriftenreihe:	Cambridge studies in advanced mathematics 144
Schlagworte:	Algebraic varieties Rings (Algebra) Ring > Mathematik
Online-Zugang:	BSB01 FHN01 UBR01 URL des Erstveröffentlichers
Zusammenfassung:	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
Beschreibung:	1 online resource (viii, 530 Seiten)
ISBN:	9781139175852
DOI:	10.1017/CBO9781139175852

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Datensatz im Suchindex

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author	Arzhantsev, Ivan Derenthal, Ulrich 1978- Hausen, Jürgen Laface, Antonio
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doi_str_mv	10.1017/CBO9781139175852
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isbn	9781139175852
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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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