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The mixed Hodge structure on the fundamental group of a punctured Riemann surface |
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| Authors: | Rainer H. Kaenders |
| Affiliation: | Mathematisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitäts- straße, 40225 Düsseldorf, Germany |
| Abstract: | Given a compact Riemann surface |
| Keywords: | |
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of genus 
and distinct points 
and 
on 
, we consider the non-compact Riemann surface 
with basepoint 
. The extension of mixed Hodge structures associated to the first two steps of 
is studied. We show that it determines the element 
in 
, where 
represents the canonical divisor of 
as well as the corresponding extension associated to 
. Finally, we deduce a pointed Torelli theorem for punctured Riemann surfaces.