Enriques Surfaces and jacobian elliptic K3 surfaces

Details Enriques Surfaces and jacobian elliptic K3 surfaces Enriques Surfaces and jacobian elliptic K3 surfaces

2009-12-03

arxiv.org/abs/0912.0608v2

Mathematics

Algebraic Geometry

35 pages, 6 figures; v2: minor additions and corrections

Scientific paper

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.

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