an:06963141
Zbl 06963141
Kozlowski, A.; Yamaguchi, K.
The homotopy type of spaces of rational curves on a toric variety
EN
Topology Appl. 249, 19-42 (2018).
00417668
2018
j
55P10 55R80 55P35 14M25
polyhedral product; fan; toric variety; primitive generator; holomorphic map; homotopy equivalence; Vassiliev spectral sequence
Summary: 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.