Witten's top Chern class via cosection localization

• 成果类型: Article
• 署名作者: Chang, Huai-Liang; Li, Jun; Li, Wei-Ping
• 署名单位: Hong Kong University of Science & Technology; Fudan University; Stanford University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0549-5
• 发表日期: 2015
• 页码: 1015-1063
• 关键词: higher spin curves; twisted curves; MODULI SPACES; K-THEORY; stacks; cycles

摘要

For a Landau-Ginzburg space , we construct Witten's top Chern class as an algebraic cycle using cosection localized virtual cycles in the case where all sectors are narrow, verify all axioms of this class, and derive an explicit formula for it in the free case. We prove that this construction is equivalent to the constructions of Polishchuk-Vaintrob, Chiodo, and Fan-Jarvis-Ruan.