The moduli space of Riemann surfaces is Kahler hyperbolic
| dc.creator | McMullen, Curtis T. | |
| dc.date | 2000-10-02 | |
| dc.date.accessioned | 2026-07-07T04:37:48Z | |
| dc.date.available | 2026-07-07T04:37:48Z | |
| dc.description | Let $\cM_{g,n}$ be the moduli space of Riemann surfaces of genus $g$ with $n$ punctures. From a complex perspective, moduli space is hyperbolic. For example, $\cM_{g,n}$ is abundantly populated by immersed holomorphic disks of constant curvature -1 in the Teichmüller (=Kobayashi) metric. When $r=\dim_{\cx} \cM_{g,n}$ is greater than one, however, $\cM_{g,n}$ carries no complete metric of bounded negative curvature. Instead, Dehn twists give chains of subgroups $\zed^r \subset π_1(\cM_{g,n})$ reminiscent of flats in symmetric spaces of rank $r>1$. In this paper we introduce a new Kähler metric on moduli space that exhibits its hyperbolic tendencies in a form compatible with higher rank. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0010022 | |
| dc.identifier | http://arxiv.org/abs/math/0010022 | |
| dc.identifier | Ann. of Math. (2) 151 (2000), no. 1, 327--357 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60036 | |
| dc.subject | Complex Variables | |
| dc.subject | 32Gxx (30F60 32Qxx) | |
| dc.title | The moduli space of Riemann surfaces is Kahler hyperbolic | |
| dc.type | text |