Ideals of Powers and Powers of Ideals : Intersecting Algebra, Geometry, and Combinatorics
2020 ed.
Book Details
Format
Paperback / Softback
Book Series
Lecture Notes of the Unione Matematica Italiana
ISBN-10
3030452468
ISBN-13
9783030452469
Edition
2020 ed.
Publisher
Springer Nature Switzerland AG
Imprint
Springer Nature Switzerland AG
Country of Manufacture
GB
Country of Publication
GB
Publication Date
May 22nd, 2020
Print length
161 Pages
Product Classification:
AlgebraNumber theoryAlgebraic geometry
Ksh 11,700.00
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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.
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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