**The Points of Quadratic Algebras
**
Michaela Vancliff

Abstract:
I plan to present recent joint work by Brad Shelton and myself, with emphasis on the following counter-intuitive
result. Let A denote a non-commutative algebra on four generators with six defining relations (each homogeneous
of degree 2), and let Z denote the locus of zeros of the defining relations of A.
If Z is finite, then the space of (1,1)-forms that vanish on Z is the span of the defining relations of A. The result
concerns the ``points'' of A and has a counterpart involving ``lines'' of A. Although the results are
non-commutative in nature, the proofs use only commutative algebra.

*created Thu Jun 1 13:07:48 PDT 2000
*