Credits: 1.00, Hours: 03.0
Time: MWF, 1:30-2:20pm (occasionally 1:15-2:30pm).
Location: Physics 205
Math 251, or consent from me.
A rough outline is as follows
In all of the above connections with algebraic geometry will be
will be used extensively.
- Gröbner and standard bases
- Standard Bases
- Free Resolutions
- Tensor Product
- Intersections, quotients, etc.
- Noether Normalization
- Primary Decomposition
- The Hilbert Polynomial
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.