抄録
The problem of approximating the infinite dimensional space of all continuous maps from an algebraic variety X to an algebraic variety Y by finite dimensional spaces of algebraic maps arises in several areas of geometry and mathematical physics. An often considered formulation of the problem (sometimes called the Atiyah–Jones problem after [1]) is to determine a (preferably optimal) integer nD such that the inclusion from this finite dimensional algebraic space into the corresponding infinite dimensional one induces isomorphisms of homology (or homotopy) groups through dimension nD, where D denotes a tuple of integers called the “degree” of the algebraic maps and nD → ∞ as D → ∞. In this paper we investigate this problem in the case when X is a real projective space and Y is a smooth compact toric variety.
