The Kodaira dimension of some moduli spaces of elliptic K3 surfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Mauro Fortuna
  • Giacomo Mezzedimi

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OriginalspracheEnglisch
Seiten (von - bis)269-294
Seitenumfang26
FachzeitschriftJournal of the London Mathematical Society
Jahrgang104
Ausgabenummer1
Frühes Online-Datum18 Jan. 2021
PublikationsstatusVeröffentlicht - 15 Juli 2021

Abstract

We study the moduli spaces of elliptic K3 surfaces of Picard number at least 3, i.e. U⊕⟨−2k⟩-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.

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The Kodaira dimension of some moduli spaces of elliptic K3 surfaces. / Fortuna, Mauro; Mezzedimi, Giacomo.
in: Journal of the London Mathematical Society, Jahrgang 104, Nr. 1, 15.07.2021, S. 269-294.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Fortuna M, Mezzedimi G. The Kodaira dimension of some moduli spaces of elliptic K3 surfaces. Journal of the London Mathematical Society. 2021 Jul 15;104(1):269-294. Epub 2021 Jan 18. doi: 10.1112/jlms.12430
Fortuna, Mauro ; Mezzedimi, Giacomo. / The Kodaira dimension of some moduli spaces of elliptic K3 surfaces. in: Journal of the London Mathematical Society. 2021 ; Jahrgang 104, Nr. 1. S. 269-294.
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