Cubic surfaces with a Galois invariant double-six

Andreas-Stephan Elsenhans; Jörg Jahnel

Displaying similar documents to “Cubic surfaces with a Galois invariant double-six”

On the order three Brauer classes for cubic surfaces

Andreas-Stephan Elsenhans, Jörg Jahnel (2012)

Open Mathematics

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We describe a method to compute the Brauer-Manin obstruction for smooth cubic surfaces over ℚ such that Br(S)/Br(ℚ) is a 3-group. Our approach is to associate a Brauer class with every ordered triplet of Galois invariant pairs of Steiner trihedra. We show that all order three Brauer classes may be obtained in this way. To show the effect of the obstruction, we give explicit examples.

Arithmetic on singular cubic surfaces

Daniel F. Coray (1976)

Compositio Mathematica

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Real quartic surfaces containing 16 skew lines.

Nieto, Isidro (2004)

International Journal of Mathematics and Mathematical Sciences

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On the fundamental units of some cubic orders generated by units

Jun Ho Lee, Stéphane R. Louboutin (2014)

Acta Arithmetica

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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...