2017/11/15 by Yuuki Tadokoro, Tadokoro, Yuuki
Mathematics · #14H30 #14H50 #30F30 #32G15 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.CV #math.GT #msc:14H30 #msc:14H50 #msc:30F30 #msc:32G15
paper · pdf · doi:10.48550/arxiv.1711.05455
15 pages
openalex publication_date 2017/11/15 · openalex created_date 2017/12/04 · arxiv created 2018/09/07 · arxiv updated 2018/09/10 · openalex updated_date 2026/07/28
The period for a compact Riemann surface, defined by the integral of differential 1-forms, is a classical complex analytic invariant, strongly related to the complex structure of the surface. In this paper, we treat another complex analytic invariant called the pointed harmonic volume. As a natural extension of the period defined using Chen's iterated integrals, it captures more detailed information of the complex structure. It is also one of a few explicitly computable examples of complex analytic invariants. We obtain its new value for a certain pointed hyperelliptic curve. An application of the pointed harmonic volume is presented. We explain the relationship between the harmonic volume and first extended Johnson homomorphism on the mapping class group of a pointed oriented closed surface.