The homotopy type of spaces of rational curves on a toric variety. (English) Zbl 1507.55012
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. G. Segal [Acta Math. 143, 39–72 (1979; Zbl 0427.55006)] investigated the homotopy type of spaces of holomorphic maps on complex projective spaces and M. A. Guest [ibid. 174, No. 1, 119–145 (1995; Zbl 0826.14035)] generalized Segal’s result for compact smooth toric varieties. Recently J. Mostovoy and E. Munguía-Villanueva [Rev. Colomb. Mat. 48, No. 1, 41–53 (2014; Zbl 1350.14037)] improved the homology stability dimension obtained by Guest. In this paper we generalize their result for certain non-compact smooth toric varieties by the careful analysis of toric varieties with the scanning maps.
MSC:
| 55P10 | Homotopy equivalences in algebraic topology |
| 55R80 | Discriminantal varieties and configuration spaces in algebraic topology |
| 55P35 | Loop spaces |
| 14M25 | Toric varieties, Newton polyhedra, Okounkov bodies |
Keywords:
polyhedral product; fan; toric variety; primitive generator; holomorphic map; homotopy equivalence; Vassiliev spectral sequenceReferences:
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