Logarithmic Gromov–Witten theory with expansions

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-03-21 DOI:10.14231/ag-2022-022

Dhruv Ranganathan

引用次数: 46

Abstract

We construct a version of relative Gromov-Witten theory with expanded degenerations in the normal crossings setting and establish a degeneration formula for the resulting invariants. Given a simple normal crossings pair $(X,D)$, we construct virtually smooth and proper moduli spaces of curves in $X$ with prescribed boundary conditions along $D$. Each point in such a moduli space parameterizes maps from nodal curves to expanded degenerations of $X$ that are dimensionally transverse to the strata. We use the expanded formalism to reconstruct the virtual class attached to a tropical map in terms of spaces of maps to expansions attached to the vertices.

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带展开式的对数Gromov-Witten理论

我们构造了一个具有扩展退化的相对Gromov-Witten理论，并建立了退化公式。给定一个简单的法向交叉对$(X,D)$，我们在$X$上沿$D$构造具有规定边界条件的曲线的虚光滑模空间。模空间中的每个点都参数化了从节点曲线到X扩展退化的映射，X扩展退化在维度上横向于地层。我们使用扩展的形式来重建虚拟类附加到热带地图的地图空间扩展附加到顶点。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.