Definition

Base field and differential varieties Unless stated otherwise, our objects are defined over a base differentially closed field F | = DCF0. (Most of what we say generalizes to the partial case, however.) We view F as being a subfield of a large differentially closed field U, though this universal domain rarely shows up explicitly. The closed sets in the Kolchin topology on Pn(U) that we consider are defined by δ-homogeneous polynomials in n + 1 variables over F; e.g., x ′1x0 − x1x ′0. These solution sets are projective differential algebraic varieties. Projective closure is tricky. As in the algebraic case, the closure may be smaller than the set defined by the δ-homogenization of the defining polynomials. William Simmons A differential algebra sampler 2 Complete differential varietie