Graduate Texts in Mathematics

Miller, Ezra; Sturmfels, Bernd

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.

Details

Published by: Springer

Publication Date: 2005-06-21

Format: Paperback

ISBN-13: 9780387237077

DOI: 10.1007/b138602

Dimensions: 235cm x155cm

Pages: 420