The Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface

dc.creatorKaenders, Rainer H.
dc.date1999-02-01
dc.date.accessioned2026-07-07T05:27:44Z
dc.date.available2026-07-07T05:27:44Z
dc.descriptionGiven a compact Riemann surface $\bar{X}$ of genus $g$ and a point $q$ on $\bar{X}$, we consider $X:=\bar{X}\setminus\{q\}$ with a basepoint $p\in X$. The extension of mixed Hodge structures, given by the weights -1 and -2, of the mixed Hodge structure on the fundamental group (in the sense of Hain) is studied. We show that it naturally corresponds on the one hand to the element $(2g q-2 p-K)$ in $\Pic^0(\bar{X})$, where $K$ represents the canonical divisor, and on the other hand to the respective extension of $\bar{X}$. Finally, we prove a pointed Torelli theorem for punctured Riemann surfaces.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/math/9902003
dc.identifierhttp://arxiv.org/abs/math/9902003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78029
dc.subjectAlgebraic Geometry
dc.subject14H40; 14H30; 14F35
dc.titleThe Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface
dc.typetext

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