# Combinatorial Commutative Algebra

## Springer Graduate Texts in Math, Vol. 227

### Publication year: 2004

Even though we can't make changes to the first printing of the
published version, we still want your comments and corrections! That
way, future published printings will be improved over this first
printing. Please do take a look at the **CURRENT LIST OF CORRECTIONS
** (in TeX, DVI, gzipped
PostScript, or PDF) and email Bernd or
me all your comments and corrections.

Springer does not allow us to make the book available online anymore,
because it is now available in print. You can, however, download just
the title page, preface, and contents as a PDF file or a PostScript file. Alternatively, you
can download the frontmatter and backmatter section by section---see
below.

The book is split into three Parts:

The text is subdivided more finely as follows:

Chapter 1. **Squarefree monomial ideals**

Chapter 2. **Borel-fixed monomial ideals**

Chapter 3. **Three-dimensional staircases**

Chapter 4. **Cellular resolutions**

Chapter 5. **Alexander duality**

Chapter 6. **Generic monomial ideals**

Chapter 7. **Semigroup algebras**

Chapter 8. **Multigraded polynomial rings**

Chapter 9. **Syzygies of lattice ideals**

Chapter 10. **Toric varieties**

Chapter 11. **Irreducible and injective resolutions**

Chapter 12. **Ehrhart polynomials**

Chapter 13. **Local cohomology**

Chapter 14. **Plücker coordinates**

Chapter 15. **Matrix Schubert varieties**

Chapter 16. **Antidiagonal initial ideals**

Chapter 17. **Minors in matrix products**

Chapter 18. **Hilbert schemes of points**

The back-cover blurb reads:

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.

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