Torelli theorem for the moduli spaces of connections on a Riemann surface
| dc.creator | Biswas, Indranil | |
| dc.creator | Munoz, Vicente | |
| dc.date | 2005-12-12 | |
| dc.date | 2007-02-05 | |
| dc.date.accessioned | 2026-07-07T07:44:29Z | |
| dc.date.available | 2026-07-07T07:44:29Z | |
| dc.description | Let $(X,x_0)$ be any one--pointed compact connected Riemann surface of genus $g$, with $g\geq 3$. Fix two mutually coprime integers $r>1$ and $d$. Let ${\mathcal M}_X$ denote the moduli space parametrizing all logarithmic $\text{SL}(r,{\mathbb C})$--connections, singular over $x_0$, on vector bundles over $X$ of degree $d$. We prove that the isomorphism class of the variety ${\mathcal M}_X$ determines the Riemann surface $X$ uniquely up to an isomorphism, although the biholomorphism class of ${\mathcal M}_X$ is known to be independent of the complex structure of $X$. The isomorphism class of the variety ${\mathcal M}_X$ is independent of the point $x_0 \in X$. A similar result is proved for the moduli space parametrizing logarithmic $\text{GL}(r,{\mathbb C})$--connections, singular over $x_0$, on vector bundles over $X$ of degree $d$. | |
| dc.description | 25 pages, no figures; v2. Revised version. To appear in Topology | |
| dc.identifier | https://arxiv.org/abs/math/0512236 | |
| dc.identifier | http://arxiv.org/abs/math/0512236 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123211 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 14H60; 14D20; 14C34 | |
| dc.title | Torelli theorem for the moduli spaces of connections on a Riemann surface | |
| dc.type | text |