Gvirtz-Chen, D. and Mezzedimi, G. (2023) A Hilbert irreducibility theorem for Enriques surfaces. Transactions of the American Mathematical Society, 376(6), pp. 3867-3890. (doi: 10.1090/tran/8831)
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Abstract
We define the over-exceptional lattice of a minimal algebraic surface of Kodaira dimension . 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 greater than or equal to 6 apart from a finite list of geometric Picard lattices. Concretely, we prove that such surfaces over finitely generated fields of characteristic 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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Gvirtz, Dr Damian |
| Authors: | Gvirtz-Chen, D., and Mezzedimi, G. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Transactions of the American Mathematical Society |
| Publisher: | American Mathematical Society (AMS) |
| ISSN: | 0002-9947 |
| ISSN (Online): | 1088-6850 |
| Published Online: | 21 March 2023 |
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