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This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.
List of contents
Introduction; 1. Basic concepts; 2. Toric varieties and Gale duality; 3. Cox rings and combinatorics; 4. Selected topics; 5. Surfaces; 6. Arithmetic applications.
About the author
Ivan Arzhantsev received his doctoral degree in 1998 from Lomonosov Moscow State University and is a professor in its department of higher algebra. His research areas are algebraic geometry, algebraic groups and invariant theory.Ulrich Derenthal received his doctoral degree in 2006 from Universität Göttingen. He is a professor of mathematics at Ludwig-Maximilians-Universität München. His research interests include arithmetic geometry and number theory.Jürgen Hausen received his doctoral degree in 1995 from Universität Konstanz. He is a professor of mathematics at Eberhard-Karls-Universität Tübingen. His field of research is algebraic geometry, in particular algebraic transformation groups, torus actions, geometric invariant theory and combinatorial methods.Antonio Laface received his doctoral degree in 2000 from Università degli Studi di Milano. He is an associate professor of mathematics at Universidad de Concepción. His field of research is algebraic geometry, more precisely linear systems and algebraic surfaces and their Cox rings.
Summary
This book gives a systematic and self-contained introduction to Cox rings, which allows for explicit treatment of advanced topics in algebraic geometry. It provides students and researchers with a straightforward guide to this field of research. Applications in algebraic and arithmetic geometry are discussed.
