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
DOI:
https://doi.org/10.1090/S0002-9947-1981-0603764-X
MathSciNet review:
603764
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Abstract | References | Similar Articles | Additional Information
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