The homotopy type of spaces of rational curves on a toric variety

Abstract

Spaces of holomorphic maps from the Riemann sphere to various complex manifolds have played an important role in several areas of mathematics (e.g. linear control theory and mathematical physics ([2], [3])). G. Segal [22] investigated the homotopy type of spaces of holomorphic maps on complex projective spaces and M. Guest [10] generalized Segal's result for compact smooth toric varieties. Recently Mostovoy–Villanueva [20] improved the homology stability dimension obtained by Guest. In this paper we generalize their result [20] for certain non-compact smooth toric varieties by the careful analysis of toric varieties with the scanning maps.