Spaces of non-resultant systems of bounded multiplicity determined by a toric variety

TL;DR

This paper generalizes the homotopy stability theorem for the space of non-resultant systems of bounded multiplicity from projective space to arbitrary non-singular toric varieties, expanding understanding of their topological structure.

Contribution

It extends the homotopy stability theorem and explicit homotopy type determination from projective space to all non-singular toric varieties.

Findings

Proved a homotopy stability theorem for non-singular toric varieties.

Explicitly determined the homotopy type of the space for these varieties.

Generalized previous results from projective space to a broader class of toric varieties.

Abstract

The space of non-resultant systems of bounded multiplicity for a toric variety X is a generalization of the space of rational curves on it. In our earlier work we proved a homotopy stability theorem and determined explicitly the homotopy type of this space for the case X = CP^m. In this paper we consider the case of a general non-singular toric variety and prove a homotopy stability theorem generalising the one for CP^m.