Computations of Gromov-Witten invariants of toric varieties

Abstract

We present the Julia package ToricAtiyahBott.jl, providing an easy way to perform the Atiyah-Bott formula on the moduli space of genus $0$ stable maps $\overline{M}_{0,m}(X,\beta)$ where $X$ is any smooth projective toric variety, and $\beta$ is any effective $1$-cycle. The list of the supported cohomological cycles contains the most common ones, and it is extensible. We provide a detailed explanation of the algorithm together with many examples and applications. The toric variety $X$, as well as the cohomology class $\beta$, must be defined using the package Oscar.jl.