On the Geometry of Principal Homogeneous Spaces
| dc.creator | de Jong, A. J. | |
| dc.creator | Friedman, Robert | |
| dc.date | 2008-10-15 | |
| dc.date.accessioned | 2026-07-07T10:10:23Z | |
| dc.date.available | 2026-07-07T10:10:23Z | |
| dc.description | Let $B$ be a curve defined over an algebraically closed field $k$ and let $X\to B$ be an elliptic surface with base curve $B$. We investigate the geometry of everywhere locally trivial principal homogeneous spaces for $X$, i.e. elements of the Tate-Shafarevich group. If $Y$ is such a principal homogeneous space of order $n$, we find strong restrictions on the $\mathbb{P}^{n-1}$ bundle over $B$ into which $Y$ embeds. Examples for small values of $n$ show that, in at least some cases, these restrictions are sharp. Finally, we determine these bundles in case $k$ has characteristic zero, $B = \mathbb{P}^1$, and $X$ is generic in a suitable sense. | |
| dc.description | 49 pages | |
| dc.identifier | https://arxiv.org/abs/0810.2687 | |
| dc.identifier | http://arxiv.org/abs/0810.2687 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171590 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J27 | |
| dc.title | On the Geometry of Principal Homogeneous Spaces | |
| dc.type | text |