Combinatorial Commutative Algebra

Graduate Texts in Mathematics #227

by Ezra Miller, Bernd Sturmfels

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.

Genres: Mathematics

423 pages, Kindle Edition

First published December 21, 2004

About the author

Ezra Matthew Miller is an American actor, known for his roles in the films City Island (2009), Another Happy Day (2011), and We Need to Talk About Kevin (2011). He starred in the 2012 teen drama The Perks of Being a Wallflower, with Logan Lerman and Emma Watson, and has signed on to play the role of Léon Dupuis in Sophie Barthes' adaptation of the Gustave Flaubert novel Madame Bovary.