Hilbert property for double conic bundles and del Pezzo varieties

In this paper we prove that, over a Hilbertian ground field, surfaces with two conic fibrations whose fibres have non-zero intersection product have the Hilbert property. We then give an application of this result, namely the verification of the Hilbert property for certain del Pezzo varieties.

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Received 30 April 2019

Accepted 22 August 2019

Published 24 May 2022