On extra-special Enriques surfaces

We define the over-exceptional lattice of a minimal algebraic surface of Kodaira dimension 0 0 . Bounding the rank of this object, we prove that a conjecture by Campana [Ann. Inst. Fourier (Grenoble) 54 (2004), pp. 499–630] and Corvaja–Zannier [Math. Z. 286 (2017), pp. 579–602] holds for Enriques surfaces, as well as K3 surfaces of Picard rank ≥ 6 \geq 6 apart from a finite list of geometric Picard lattices. Concretely, we prove that such surfaces over finitely generated fields of characteristic 0 0 satisfy the weak Hilbert Property after a finite field extension of the base field. The degree of the field extension can be uniformly bounded.

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Nodal Enriques surfaces are Reye congruences

Martin,

Mezzedimi,

Veniani

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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On extra-special Enriques surfaces

Abstract: We refine Cossec and Dolgachev’s classification of extra-special Enriques surfaces, providing a complete and concise proof.

Cited by 3 publications

References 27 publications

A Computational View on the Non-degeneracy Invariant for Enriques Surfaces

A Computational View on the Non-degeneracy Invariant for Enriques Surfaces

A Hilbert irreducibility theorem for Enriques surfaces

Nodal Enriques surfaces are Reye congruences

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