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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