超椭圆曲线的调和函数

具有Weierstrass基点的超椭圆曲线的点调和体积

The pointed harmonic volumes of hyperelliptic curves with Weierstrass base points

给出了以Weierstrass基点为基点的超椭圆曲线的点调和体积的显式计算，并将其转化为一个组合公式.

Pointed harmonic volume and its relation to the extended Johnson homomorphism

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…

Harmonic volume and its applications

The period is a classical complex analytic invariant for a compact Riemann surface defined by integration of differential 1-forms. It has a strong relationship with the complex structure of the surface. In this chapter, we review another complex analytic invariant called the harmonic volume. It is a natural extension of the period defined using Chen's iterated integrals and captures more detailed information of the complex structure. It is also one of a few explicitly computable examples of complex analytic invariants. As an application, we give an algorithm in proving nontriviality for a clas…