## Title data

Bauer, Ingrid ; Stoll, Michael:

**Geometry and arithmetic of primary Burniat surfaces.**

*In:* Mathematische Nachrichten.
Vol. 290
(October 2017)
Issue 14–15
.
- pp. 2132-2153.

ISSN 1522-2616

DOI: https://doi.org/10.1002/mana.201600282

Review: |

## Related URLs

## Project information

Project title: |
Project's official title Project's id Forschergruppe 790 Classification of Algebraic Surfaces and Compact Complex Manifolds FOR 790/2 No information Sto 299/9-1 |
---|---|

Project financing: |
Deutsche Forschungsgemeinschaft |

## Abstract in another language

We study the geometry and arithmetic of so-called primary Burniat surfaces, a family of surfaces of general type arising as smooth bidouble covers of a del Pezzo surface of degree 6 and at the same time as étale quotients of certain hypersurfaces in a product of three elliptic curves. We give a new explicit description of their moduli space and determine their possible automorphism groups. We also give an explicit description of the set of curves of geometric genus 1 on each primary Burniat surface. We then describe how one can try to obtain a description of the set of rational points on a given primary Burniat surface S defined over math formula. This involves an explicit description of the relevant twists of the étale covering of S coming from the second construction mentioned above and methods for finding the set of rational points on a given twist.