Welcome to the section of commalg.org consisting, loosely, of survey articles related to commutative algebra. We say “loosely” because it contains other gems from the internet like books and articles about commutative algebraists.

We’re always happy to hear from you if you’ve got suggestions for other articles you think we should point to — just let us know!

Here is a list from David Eisenbud and Craig Huneke of “Accessible papers in commutative algebra”. It’s a great resource; thanks, David and Craig!

## Algebraic Geometry

- Aaron Bertram:
- Manuel Blickle, Hélène Esnault, Kay Rülling: Characteristic 0 and p analogies, and some motivic cohomology
- Manuel Blickle: A Short Course on Geometric Motivic Integration
- Manuel Blickle and Robert Lazarsfeld: An informal introduction to multiplier ideals
- Jaydeep V. Chipalkatti: Notes on Grassmannians and Schubert Varieties
- David A. Cox:
- Cox, Little and O’Shea:
- Cox, Little and Schenck: Toric Varieties
- David Eisenbud:
- David Eisenbud, Mark Green and Joe Harris: Cayley-Bacharach theorems and conjectures
- David Eisenbud and Joe Harris: Progress in the theory of complex algebraic curves
- David Eisenbud and Jee-Heub Koh: Remarks on points in a projective space
- Alexander Grothendieck:
- Mark Haiman: Commutative algebra of N points in the plane
- Peter Jørgensen: Non-commutative projective geometry
- Juan Migliore: Experiments in Commutative Algebra and Algebraic Geometry
- Ezra Miller: What is … a toric variety?
- J. S. Milne: Algebraic Geometry Course Notes
- Jürgen Richter-Gebert, Bernd Sturmfels, Thorsten Theobald: First steps in tropical geometry
- Karen E. Smith:
- David Speyer and Bernd Sturmfels: Tropical mathematics
- Charles Weibel:

## Lie Algebras

- Joris van Hoboken: Platonic solids, binary polyhedral groups,

Kleinian singularities and Lie algebras of type A, D, E - Victor Kac: Lie Algebras Course Notes

## Miscellaneous

- Free Online MIT Course Materials
- The Rising Sea: Notes by Daniel Murfet
- Apostolos Beligiannis and Idun Reiten: Homological aspects of torsion theories
- Dave Benson:
- Edward Green, Idun Reiten and Øyvind Solberg: Dualities on generalized Koszul algebras
- Dragan Milicic:
- L. J. Ratliff, Jr.: A brief history and survey of the catenary chain conjectures

## Homological Conjectures

- Mel Hochster: Some Expository Manuscripts
- Paul Roberts:

## Tight Closure

- Mel Hochster: Some Expository Manuscripts
- Karen E. Smith: An Introduction to Tight Closure
- Irena Swanson: Ten lectures on tight closure

## Resolutions and Homological Dimensions

- Lucho Avramov:
- David Eisenbud:
- Vladimir Maşek: Gorenstein dimension of modules
- Claudia Miller: The Frobenius endomorphism and homological dimensions
- Roger Wiegand: What is… a Syzygy?

## Connections with Algebraic Topology

- J. P. C. Greenlees:
- Notes from the Summer School on the Interactions between Homotopy Theory and Algebra, University of Chicago, July 26 to August 6, 2004

## Multiplicities and Hilbert Functions

- Irena Peeva and Mike Stillman: Open problems on syzygies and Hilbert functions
- Irena Swanson: Multi-graded Hilbert functions and mixed multiplicities

## Ideal Theory

- Irena Swanson: Primary decompositions
- Stefania Gabelli: Characterizing integral domains by semigroups of ideals – Notes for an advanced course in Ideal Theory

## Computation and Gröbner Bases

- David A. Cox:
- Cox, Little and O’Shea: Ideals, Varieties, and Algorithms
- David Eisenbud: Open problems in computational algebraic geometry
- David Eisenbud, Dan Grayson, Mike Stillman, and Bernd Sturmfels: Computations in algebraic geometry with Macaulay 2
- Juan Migliore: Experiment in Commutative Algebra and Algebraic Geometry
- Bernd Sturmfels: What is a Grobner basis?

## Integral Closure

- Swanson and Huneke: Integral Closure of Ideals, Rings, and Modules

## Factorization

- Jim Coykendall and Scott Chapman: Half-factorial domains, a survey
- Jim Coykendall: Extensions of half-factorial domains
- Marco Fontana and Muhammad Zafrullah: On v-domains: a survey
- Muhammad Zafrullah:

## K-Theory

- Dan Grayson: A Brief Introduction to Algebraic K-Theory
- Charles Weibel:

## Tributes

- Lucho Avramov: The Work of Jan-Erik roos on the Cohomology of Commutative Rings
- David Eisenbud:

## Connections with Combinatorics

- Winfried Bruns and Udo Vetter: Determinantal Rings
- David Eisenbud: Introduction to algebras with straightening laws
- Ezra Miller and David Perkinson: Eight Lectures on Monomial Ideals
- Ezra Miller and Vic Reiner: What is geometric combinatorics?—An overview of the graduate summer school

## (Co)homology

- Craig Huneke: Lectures on Local Cohomology (Appendix by Amelia Taylor)
- Cristodor Ionescu: Hochschild (Co)homology in Commutative Algebra. A Survey

## Applications

- N. Eriksson, K. Ranestad, B. Sturmfels and S. Sullivant: Phylogenetic algebraic geometry
- Lior Pachter and Bernd Sturmfels: Tropical geometry of statistical models
- Bernd Sturmfels:

## Interviews

- David Eisenbud, interviewed by Sara Robinson: Mathematics comes from many sources
- Allyn Jackson: Presidential views: Interview with David Eisenbud
- Allyn Jackson: Presidential reflections: Interview with David Eisenbud