The Kodaira dimension of some moduli spaces of elliptic K3 surfaces

Media type: Text; E-Article
Title: The Kodaira dimension of some moduli spaces of elliptic K3 surfaces
Contributor: Fortuna, Mauro [Author]; Mezzedimi, Giacomo [Author]
imprint: Chichester : John Wiley and Sons Ltd, 2021
Published in: Journal of the London Mathematical Society 104 (2021), Nr. 1
Issue: published Version
Language: English
DOI: https://doi.org/10.15488/10567; https://doi.org/10.1112/jlms.12430
ISSN: 0024-6107
Keywords: 32M15 ; Jordan algebras ; 14M20 (primary) ; 14J27 ; elliptic or Calabi-Yau fibrations ; analytic theory ; 32N15 (secondary) ; Hermitian symmetric spaces ; 14J15 ; Elliptic surfaces ; surfaces and Enriques surfaces ; 14J28 ; Rational and unirational varieties ; bounded symmetric domains
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Description: We study the moduli spaces of elliptic K3 surfaces of Picard number at least 3, that is, U ⊕ ⟨ − 2 k ⟩ -polarized K3 surfaces. Such moduli spaces are proved to be of general type for k ⩾ 220 . The proof relies on the low-weight cusp form trick developed by Gritsenko, Hulek and Sankaran. Furthermore, explicit geometric constructions of some elliptic K3 surfaces lead to the unirationality of these moduli spaces for k < 11 and for 19 other isolated values up to k = 64 .
Access State: Open Access
Rights information: Attribution (CC BY)

The Kodaira dimension of some moduli spaces of elliptic K3 surfaces - [published Version]