Details
| Original language | English |
|---|---|
| Pages (from-to) | 269-294 |
| Number of pages | 26 |
| Journal | Journal of the London Mathematical Society |
| Volume | 104 |
| Issue number | 1 |
| Early online date | 18 Jan 2021 |
| Publication status | Published - 15 Jul 2021 |
Abstract
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In: Journal of the London Mathematical Society, Vol. 104, No. 1, 15.07.2021, p. 269-294.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The Kodaira dimension of some moduli spaces of elliptic K3 surfaces
AU - Fortuna, Mauro
AU - Mezzedimi, Giacomo
N1 - Funding information: The first author acknowledges partial support from the DFG Grant Hu 337/7?1.
PY - 2021/7/15
Y1 - 2021/7/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85099483483&partnerID=8YFLogxK
U2 - 10.1112/jlms.12430
DO - 10.1112/jlms.12430
M3 - Article
AN - SCOPUS:85099483483
VL - 104
SP - 269
EP - 294
JO - Journal of the London Mathematical Society
JF - Journal of the London Mathematical Society
SN - 0024-6107
IS - 1
ER -