The Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface
| dc.creator | Kaenders, Rainer H. | |
| dc.date | 1999-02-01 | |
| dc.date.accessioned | 2026-07-07T05:27:44Z | |
| dc.date.available | 2026-07-07T05:27:44Z | |
| dc.description | Given 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.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/9902003 | |
| dc.identifier | http://arxiv.org/abs/math/9902003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78029 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H40; 14H30; 14F35 | |
| dc.title | The Mixed Hodge Structure on the Fundamental Group of a Punctured Riemann Surface | |
| dc.type | text |