环状变体的格罗莫夫-维滕不变式计算

Pub Date : 2024-04-23 DOI:10.1016/j.jsc.2024.102330

Giosuè Muratore

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引用次数: 0

摘要

我们介绍了 Julia 软件包 ToricAtiyahBott.jl，它提供了一种在 0 属稳定映射 M‾0,m(X,β) 的模空间上执行 Atiyah-Bott 公式的简便方法，其中 X 是任意光滑射影环综，β 是任意有效的 1 循环。支持的同调循环列表包含了最常见的循环，而且是可扩展的。我们对算法进行了详细解释，并列举了许多例子和应用。环综 X 以及同调类 β 必须使用 Oscar.jl 软件包定义。

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Computations of Gromov–Witten invariants of toric varieties

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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