0. Tutorial on elementary applications of 
Groebner bases.

1. Canonical embeddings of plane curves.

2. Ext of line bundles on an ell curve and
vector bundles of rank 2 on the curve.

2A. Elliptic scrolls and coho of line bundles
on same. (Hodge diamond, Np properties)

3. Intersection of a curve with a divisor.
Playing with rational normal scrolls.  

4. 27 lines on a cubic; adjoint representation
of the points in P2 and the cubic.

5. 28 bitangents of
a plane quartic.

6.  Gale transform of a set of points.  
Examples.

7.  Rational normal curve through r+3 points.
Problem of finding the representation of a 
scroll, given a ruling or given a rank 3 
quadric or given a codim 2 plane meeting the
scroll appropriately.

8.  Reyes' correspondence:  3x3 minors of 
generic symm matrix; or ... 

9.  Subvarieties of G(2,4); bidegrees etc.

10.  Tangent cone, normal cone, Rees alg.

11.  Multigraded examples. Commutative algebra
(Spanish complex)

12.  Multigraded examples: Geometry.  Yau's
example of C-Y 3fold:  compute the coho of the
tangent bundle to a 3,3 divisor (smooth) on
P2 x P2.

13.  Multiplicative structure on a free resolution.

14. Fano Varieties.  Distinguishing a rational
normal scroll from a Veronese surface.

15. Adjoining a root to a field. Adjoining

16.  Using parameters.


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