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

TL;DR

This paper extends the understanding of the homotopy type of spaces of holomorphic rational curves to certain non-compact smooth toric varieties, building on prior foundational work in the field.

Contribution

It generalizes previous results to include non-compact smooth toric varieties, broadening the scope of homotopy type analysis for holomorphic curves.

Findings

Established the homotopy type for spaces of rational curves on non-compact toric varieties.

Extended stability dimension results to a broader class of toric varieties.

Connected the homotopy theory of holomorphic curves with geometric properties of toric varieties.

Abstract

Spaces of holomorphic maps from the Riemann sphere to various complex manifolds (holomorphic curves ) have played an important role in several area of mathematics. In a seminal paper G. Segal investigated the homotopy type of holomorphic curves on complex projective spaces and M. Guest on compact smooth toric varieties.. Recently Mostovoy and Villanueva, obtained a far reaching generalisation of these results, and in particular (for holomorphic curves) improved the stability dimension obtained by Guest. In this paper, we generalize their result to holomorphic curves, on certain non-compact smooth toric varieties.