Ideals of Powers and Powers of Ideals (eBook)

Intersecting Algebra, Geometry, and Combinatorics

Enrico Carlini, Huy Tài Hà, Brian Harbourne, Adam Van Tuyl (Autoren)

eBook Download: PDF

2020 | 1st ed. 2020
XIX, 161 Seiten
Springer International Publishing (Verlag)
978-3-030-45247-6 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 21.5.2020
• Reihe/Serie: Lecture Notes of the Unione Matematica Italiana
• Reihe/Serie: Lecture Notes of the Unione Matematica Italiana
• Zusatzinfo: XIX, 161 p. 21 illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Associated Primes • Castelnuovo-Mumford regularity • Containment Problem • Edge and Cover Ideals of Finite Simple Graphs • monomial ideals • Powers of Ideals • Symbolic Defect • Symbolic Powers of Ideals • Unexpected Curves and Hypersurfaces • Waldschmidt Constant • Waring Problems
• ISBN-10: 3-030-45247-6 / 3030452476
• ISBN-13: 978-3-030-45247-6 / 9783030452476