Ideals of Powers and Powers of Ideals: Intersecting Algebra, Geometry, and Combinatorics (Lecture Notes of the Unione Matematica Italiana, Band 27) - Softcover

Carlini, Enrico; Hà, Huy Tài; Harbourne, Brian; Van Tuyl, Adam

Softcover

ISBN 10: 3030452468 ISBN 13: 9783030452469

Verlag: Springer, 2020

Inhaltsangabe

This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning  our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms.  Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.

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Über die Autorin bzw. den Autor

Cristiano Bocci is a full Professor in geometry at the Department of Information Engineering and Mathematics of the Università di Siena, Italy. His research interests focus on Algebraic Geometry, Combinatorial Commutative Algebra, Algebraic Statistics and Biomathematics. Enrico Carlini is a full Professor in geometry at the Department of Mathematical Sciences of the Politecnico di Torino, in Turin, Italy. His research interests focus on the interactions between Algebraic Geometry and Commutative Algebra and on their applications.

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This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning  our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms.  Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2020
• Sprache: Englisch
• ISBN 10: 3030452468
• ISBN 13: 9783030452469
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 184
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland