Department of Mathematics  

Duke University




    

Kummer Surface

Commutative Algebra
(Math 252)

Spring 2009

Instructor: Paul Aspinwall

Credits: 1.00, Hours: 03.0

Time: MWF, 1:30-2:20pm (occasionally 1:15-2:30pm).

Location: Physics 205

Requirements

Exams


Prerequisits

Math 251, or consent from me.

Homework

Synopsis

A rough outline is as follows
  • Ideals
    • Localization
    • Gröbner and standard bases
  • Modules
    • Standard Bases
    • Free Resolutions
    • Tensor Product
    • Intersections, quotients, etc.
  • Noether Normalization
  • Primary Decomposition
  • The Hilbert Polynomial
In all of the above connections with algebraic geometry will be discussed. Singular will be used extensively.

Textbooks

The course will be based on:
  • G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, Springer 2002.

It may also be useful to refer to

  • D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms, Springer 1992.
  • David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer 1999.
  • M. Atiyah, MacDonald, Introduction to Commutative Algebra, Addison-Wesley 1969.
  • R. Hartshorne, Algebraic Geometry, Springer 1977.

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