Details
| Original language | English |
|---|---|
| Pages (from-to) | 1025-1056 |
| Number of pages | 32 |
| Journal | Mathematische Zeitschrift |
| Volume | 268 |
| Issue number | 3-4 |
| Publication status | Published - 17 Apr 2010 |
Abstract
Keywords
- Automorphism, Brauer group, Elliptic fibration, Enriques surface, K3 surface, Mordell-Weil group
ASJC Scopus subject areas
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In: Mathematische Zeitschrift, Vol. 268, No. 3-4, 17.04.2010, p. 1025-1056.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Enriques surfaces and Jacobian elliptic K3 surfaces
AU - Hulek, Klaus
AU - Schütt, Matthias
N1 - Funding information: Partial funding from DFG grant Hu 337/6-1 is gratefully acknowledged.
PY - 2010/4/17
Y1 - 2010/4/17
N2 - This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction.
AB - This paper proposes a new geometric construction of Enriques surfaces. Its starting point are K3 surfaces with jacobian elliptic fibration which arise from rational elliptic surfaces by a quadratic base change. The Enriques surfaces obtained in this way are characterised by elliptic fibrations with a rational curve as bisection which splits into two sections on the covering K3 surface. The construction has applications to the study of Enriques surfaces with specific automorphisms. It also allows us to answer a question of Beauville about Enriques surfaces whose Brauer groups show an exceptional behaviour. In a forthcoming paper, we will study arithmetic consequences of our construction.
KW - Automorphism
KW - Brauer group
KW - Elliptic fibration
KW - Enriques surface
KW - K3 surface
KW - Mordell-Weil group
UR - http://www.scopus.com/inward/record.url?scp=79960133057&partnerID=8YFLogxK
UR - https://arxiv.org/abs/0912.0608
U2 - 10.1007/s00209-010-0708-3
DO - 10.1007/s00209-010-0708-3
M3 - Article
AN - SCOPUS:79960133057
VL - 268
SP - 1025
EP - 1056
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3-4
ER -