Computations of Gromov–Witten invariants of toric varieties

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-04-23 DOI:10.1016/j.jsc.2024.102330

Giosuè Muratore

引用次数: 0

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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环状变体的格罗莫夫-维滕不变式计算

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.