Witten's top Chern class via cosection localization

2013/03/28 by Huai-Liang Chang, Jun Li, Chang, Huai-Liang +3 · 1 citation
Mathematics · Physics and Astronomy · #14N35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #math-ph #math.AG #math.MP #msc:14N35

paper · pdf · doi:10.48550/arxiv.1303.7126

35 pages

arxiv created 2013/03/28 · openalex publication_date 2013/03/28 · arxiv updated 2013/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a Landau Ginzburg space ([Cⁿ/G],W), we construct the Witten's top Chern classes as algebraic cycles via cosection localized virtual cycles in case all sectors are narrow. We verify all axioms of such classes. We derive an explicit formula of such classes in the free case. We prove that this construction is equivalent to the prior constructions of Polishchuk-Vaintrob, of Chiodo and of Fan-Jarvis-Ruan.

Citations

• The Witten equation and its virtual fundamental cycle

Cited by

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• Landau-Ginzburg/Calabi-Yau correspondence for the complete intersections X_3,3 and X_2,2,2,2

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