Ezra Miller, Bernd Sturmfels

Combinatorial Commutative Algebra (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book provides an introduction to combinatorial commutative algebra with particular emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determined rings. The eighteen chapters cover 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. Contains over 100 figures and 250 exercises.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 420
• Erscheinungstermin: 13. November 2005
• Englisch
• ISBN-13: 9780387271033
• Artikelnr.: 43728823

Autorenporträt

Ezra Miller, University of Minnesota, Minneapolis, MN, USA / Bernd Sturmfels, University of California at Berkeley, Berkeley, CA, USA

Inhaltsangabe

Monomial Ideals.- Squarefree monomial ideals.- Borel-fixed monomial ideals.- Three-dimensional staircases.- Cellular resolutions.- Alexander duality.- Generic monomial ideals.- Toric Algebra.- Semigroup rings.- Multigraded polynomial rings.- Syzygies of lattice ideals.- Toric varieties.- Irreducible and injective resolutions.- Ehrhart polynomials.- Local cohomology.- Determinants.- Plücker coordinates.- Matrix Schubert varieties.- Antidiagonal initial ideals.- Minors in matrix products.- Hilbert schemes of points.

Rezensionen

From the reviews:

"The book under review constitutes a self-contained introduction to the use of combinatorial methods in commutative algebra. ... Concrete calculations and examples are used to introduce and develop concepts. Numerous exercises provide the opportunity to work through the material and end of chapter notes comment on the history and development of the subject. The authors have provided us with a useful reference and an effective text book." (R. J. Shank, Zentralblatt MATH, Vol. 1090 (16), 2006)