Tube classes over elementary vanishing cycles

2022/05/25 by Erjuan Fu, Fu, Erjuan
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2205.12435

openalex publication_date 2022/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a closed Riemann surface. When X is embedded into a projective space, the first rational cohomology group can be concretely obtained from the monodromy in the family of its smooth hyperplane sections by C. Schnell's tube mapping. We generalize this result to the first integral homology group by relating the tube mapping with the topological Abel--Jacobi mapping. By making use of the mapping class group action, we prove that all tube classes constructed from the elementary vanishing cycles form a cofinite subgroup of the first integral homology group of X.

Related

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