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Cover: 9783031255694 | Abelian Varieties over the Complex Numbers | A Graduate Course | Lange
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Abelian Varieties over the Complex Numbers
A Graduate Course
Taschenbuch von Herbert Lange
Sprache: Englisch

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Beschreibung
This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.
The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier¿Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.
This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.
This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles.
The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier¿Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained.
This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.
Über den Autor
Herbert Lange, now retired, was a professor at the department of mathematics of the University Erlangen-Nuremberg. He has published more than 130 research papers on abelian varieties, curve theory and vector bundles on algebraic curves, as well as several books.
Zusammenfassung

Presents geometric constructions of the key abelian varieties: Jacobian, Albanese, Picard and Prym varieties

Introduces the Fourier-Mukai transform for sheaves and applies it to algebraic cycles and the Hodge conjecture

Includes more than 300 exercises of varying difficulty

Inhaltsverzeichnis
1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.
Details
Erscheinungsjahr: 2023
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Grundlehren Text Editions
Inhalt: xii
384 S.
1 s/w Illustr.
384 p. 1 illus.
ISBN-13: 9783031255694
ISBN-10: 3031255690
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lange, Herbert
Hersteller: Springer International Publishing
Springer International Publishing AG
Grundlehren Text Editions
Maße: 235 x 155 x 22 mm
Von/Mit: Herbert Lange
Erscheinungsdatum: 16.03.2023
Gewicht: 0,598 kg
Artikel-ID: 126243925
Über den Autor
Herbert Lange, now retired, was a professor at the department of mathematics of the University Erlangen-Nuremberg. He has published more than 130 research papers on abelian varieties, curve theory and vector bundles on algebraic curves, as well as several books.
Zusammenfassung

Presents geometric constructions of the key abelian varieties: Jacobian, Albanese, Picard and Prym varieties

Introduces the Fourier-Mukai transform for sheaves and applies it to algebraic cycles and the Hodge conjecture

Includes more than 300 exercises of varying difficulty

Inhaltsverzeichnis
1. Line Bundles on Complex Tori.- 2 Abelian Varieties.- 3 Moduli Spaces.- 4 Jacobian Varieties.- 5 Main Examples of Abelian Varieties.- 6 The Fourier Transform for Sheaves and Cycles.- 7 Introduction to the Hodge Conjecture for Abelian Varieties.
Details
Erscheinungsjahr: 2023
Fachbereich: Arithmetik & Algebra
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Grundlehren Text Editions
Inhalt: xii
384 S.
1 s/w Illustr.
384 p. 1 illus.
ISBN-13: 9783031255694
ISBN-10: 3031255690
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lange, Herbert
Hersteller: Springer International Publishing
Springer International Publishing AG
Grundlehren Text Editions
Maße: 235 x 155 x 22 mm
Von/Mit: Herbert Lange
Erscheinungsdatum: 16.03.2023
Gewicht: 0,598 kg
Artikel-ID: 126243925
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