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Combinatorial Commutative Algebra (Graduate Texts in Mathematics)

Combinatorial Commutative Algebra (Graduate Texts in Mathematics)
Author: Ezra Miller - Bernd Sturmfels
ISBN 13: 9780387237077
ISBN 10: 387237070
Edition: 2005
Publisher: Springer
Publication Date: 2005-06-21
Format: Paperback
Pages: 420
List Price: $59.95

Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers.