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arXiv · 2309.03741

Computations of Gromov-Witten invariants of toric varieties

Giosuè Muratore
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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 $\overline{M}_{0,m}(X,β)$ where $X$ is any smooth projective toric variety, and $β$ 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 $β$, must be defined using the package Oscar.jl.

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Giosuè Muratore. 2025-02-06. Computations of Gromov-Witten invariants of toric varieties. https://doi.org/10.1016/j.jsc.2024.102330

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