The logarithmic gauged linear sigma model

2019/06/30 by Qile Chen, Felix Janda, Yongbin Ruan · 11 citations
Mathematics · #Algebraic Geometry and Number Theory #Botany #Computer science #Discrete mathematics #Genus #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Logarithm #Mathematical analysis #Mathematics #Moduli #Pure mathematics #Sigma #Stack (abstract data type) #math.AG #msc:14D23 #msc:14N35

paper · pdf · doi:10.1007/s00222-021-01044-2

published in Inventiones mathematicae 225(3), 1077-1154 (Springer Science+Business Media) · Agrees with published version; 57 pages

openalex publication_date 2021/04/06 · arxiv created 2021/04/07 · arxiv updated 2021/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce the notion of log R-maps, and develop a proper moduli stack of stable log R-maps in the case of a hybrid gauged linear sigma model. Two virtual cycles (canonical and reduced) are constructed for these moduli stacks. The main results are two comparison theorems relating the reduced virtual cycle to the cosection localized virtual cycle, as well as the reduced virtual cycle to the canonical virtual cycle. This sets the foundation of a new technique for computing higher genus Gromov-Witten invariants of complete intersections.

Citations

• Mixed-Spin-P fields of Fermat quintic polynomials
• Phases of N = 2 theories in two dimensions
• Using stacks to impose tangency conditions on curves
• A mirror theorem for genus two Gromov-Witten invariants of quintic threefolds
• Localized Chern Characters for 2-periodic complexes
• Algebraic virtual cycles for quantum singularity theories
• Quantum singularity theory via cosection localization
• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
• BCOV's Feynman rule of quintic 3-folds
• Compactifying the space of stable maps