  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.
