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　　分類: 图书,进口原版书,科学与技术 Science & Techology ,

作者： Ezra Miller 著

出 版 社：

出版时间： 2005-6-1字数：版次： 1页数： 417印刷时间： 2005/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387237077包装： 精装内容简介

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.

目录

Ⅰ Monomial Ideals

1 Squarefree monomial ideals

1.1 Equivalent descriptions

1.2 Hilbert series

1.3 Simplicial complexes and homology

1.4 Monomial matrices

1.5 Betti numbers

Exercises

Notes

2Borel-fixed monomial ideals

2.1 Group actions

2.2 Generic initial ideals

2.3 The Eliahou-Kervaire resolution

2.4 Lex-segment ideals

Exercises

Notes

3Three-dimensional staircases

3.1 Monomial ideals in two variables

3.2 An example with six monomials

3.3 The Buchberger graph

3.4 Genericity and deformations

3.5 The planar resolution algorithm

Exercises

Notes

4Cellular resolutions

4.1 Construction and exactness

4.2 Betti numbers and K-polynomials

4.3 Examples of cellular resolutions

4.4 The hull resolution

4.5 Subdividing the simplex

Exercises

Notes

5Alexander duality

5.1 Simplicial Alexander duality

5.2 Generators versus irreducible components

5.3 Duality for resolutions

5.4 Cohull resolutions and other applications

5.5 Projective dimension and regularity

Exercises

Notes

6Generic monomial ideals

6.1 Taylor complexes and genericity

6.2 The Scarf complex

6.3 Genericity by deformation

6.4 Bounds on Betti numbers

6.5 Cogeneric monomial ideals

Exercises

Notes

Ⅱ Toric Algebra

7 Semigroup rings

7.1 Semigroups and lattice ideals

7.2 Affine semigroups and polyhedral cones

7.3 Hilbert bases

7.4 Initial ideals of lattice ideals

Exercises

Notes

8 Multigraded polynomial rings

8.1 Multigradings

8.2 Hilbert series and K-polynomials

8.3 Multigraded Betti numbers

8.4 K-polynomials in nonpositive gradings

8.5 Multidegrees

Exercises

Notes

9 Syzygies of lattice ideals

9.1 Betti numbers

9.2 Laurent monomial modules

9.3 Free resolutions of lattice ideals

9.4 Genericity and the Scarf complex

Exercises

Notes

……

ⅢDeterminants

References

Glossary of Notation

Index

 

 

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