Title data
Bauer, Ingrid ; Stoll, Michael:
Geometry and arithmetic of primary Burniat surfaces.
In: Mathematische Nachrichten.
Vol. 290
(October 2017)
Issue 14–15
.
 pp. 21322153.
ISSN 15222616
DOI: https://doi.org/10.1002/mana.201600282
Project information
Project title: 



Project financing: 
Deutsche Forschungsgemeinschaft 
Abstract in another language
We study the geometry and arithmetic of socalled 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.