Elliptic Three-folds I: Ogg-Shafarevich Theory
| dc.creator | Dolgachev, I. | |
| dc.creator | Gross, M. | |
| dc.date | 1992-10-30 | |
| dc.date | 1993-04-16 | |
| dc.date.accessioned | 2026-07-07T08:57:39Z | |
| dc.date.available | 2026-07-07T08:57:39Z | |
| dc.description | We calculate the Tate-Shafarevich group of an elliptic three-fold $f:X\rightarrow S$ when $X$ and $S$ are regular and $f$ is flat, relating it to the Brauer group of $X$ and $S$. We show that given certain hypotheses on $f$, the Tate-Shafarevich group has the interpretation of isomorphism classes of elliptic curves over the function field of $S$ which have the same jacobian as the generic fibre of $f$, and for which there exists a relatively minimal model which has no multiple fibres. We use this to give examples of elliptic fibrations with isolated multiple fibres, and also to give a new counterexample to the Luroth problem in dimension three. This is a revised, hopefully improved, version with a few extra theorems and a few errors corrected. | |
| dc.description | 39 pages, plain TeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9210009 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9210009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147052 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Elliptic Three-folds I: Ogg-Shafarevich Theory | |
| dc.type | text |