Periods of iterated integrals of holomorphic forms on a compact Riemann surface

Author:
Shu Yin Hwang Ma

Journal:
Trans. Amer. Math. Soc. **264** (1981), 295-300

MSC:
Primary 14H15; Secondary 14H20, 30F30, 32G20

MathSciNet review:
603764

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Abstract: Holomorphic forms are integrated iteratedly along paths in a compact Riemann surface of genus , thus inducing a homomorphism from the fundamental group to a proper multiplicative subgroup of the group of units in , where denotes the space of holomorphic forms on is the complex dual of , means the associated tensor algebra and 11'' means completion with respect to the natural grading. The associated homomorphisms from to reduces to the classical case when . We show that the images of are always cocompact in and are discrete for all if and only if the Jacobian variety of is isogenous to for some elliptic curve with complex multiplication.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1981-0603764-X

Keywords:
Iterated integrals,
compact Riemann surfaces,
period matrices,
Jacobian varieties,
Lie group,
holomorphic forms

Article copyright:
© Copyright 1981
American Mathematical Society