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On plane quartics with a Galois invariant Cayley octad. (English) Zbl 1473.14052

Summary: We describe a construction of plane quartics with prescribed Galois operation on the 28 bitangents, in the particular case of a Galois invariant Cayley octad. As an application, we solve the inverse Galois problem for degree two del Pezzo surfaces in the corresponding particular case.

MSC:

14H25 Arithmetic ground fields for curves
14J20 Arithmetic ground fields for surfaces or higher-dimensional varieties
14J26 Rational and ruled surfaces
14J45 Fano varieties
11G35 Varieties over global fields

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