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Bauer, Ingrid ; Stoll, Michael:
Geometry and arithmetic of primary Burniat surfaces.
In: Mathematische Nachrichten.
Bd. 290
(2017)
Heft 14–15
.
- S. 2132-2153.
ISSN 1522-2616
DOI: https://doi.org/10.1002/mana.201600282
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID Forschergruppe 790 Classification of Algebraic Surfaces and Compact Complex Manifolds FOR 790/2 Ohne Angabe Sto 299/9-1 |
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| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
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.