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Geometry and arithmetic of primary Burniat surfaces

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

Project information

Project title:
Project's official titleProject's id
Forschergruppe 790 Classification of Algebraic Surfaces and Compact Complex ManifoldsFOR 790/2
No informationSto 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.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Surface of general type; moduli space; Lang conjectures; rational points
Subject classification: Mathematics Subject Classification Code: 14G05 14J29 (14G25 14J10 14J50 14K12)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Algebraic Geometry
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Algebraic Geometry > Professorship Algebraic Geometry - Univ.-Prof. Dr. Ingrid Bauer
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 26 Oct 2017 08:08
Last Modified: 26 Oct 2017 08:08
URI: https://eref.uni-bayreuth.de/id/eprint/40177