Combinatorial Aspects of the Hilbert Scheme,

The Hilbert Scheme is a fundamental object of study in Algebraic Geometry, as it parametrizes all algebras of the form having certain properties in common. In this paper I give a description of such algebras, what properties algebras on the same Hilbert Scheme have in common, and some general properties of the Hilbert Scheme itself. I also indicate how computers become involved in solving these problems for particular algebras and particular Hilbert Schemes.