TY - JOUR

T1 - Unirational moduli spaces of some elliptic K3 surfaces

AU - Fortuna, Mauro

AU - Hoff, Michael

AU - Mezzedimi, Giacomo

N1 - Funding Information: We would like to thank Klaus Hulek and Matthias Schütt for useful discussions and for reading an early draft of this manuscript. We also thank the anonymous referee for carefully reading the paper and suggesting several improvements. The first author acknowledges partial support from the DFG Grant Hu 337/7-1.

PY - 2024/1

Y1 - 2024/1

N2 - We show that the moduli space of U⊕⟨−2k⟩-polarized K3 surfaces is unirational for k≤50 and k∉{11,35,42,48}, and for other several values of k up to k=97. Our proof is based on a systematic study of the projective models of elliptic K3 surfaces in Pn for 3≤n≤5 containing either the union of two rational curves or the union of a rational and an elliptic curve intersecting at one point.

AB - We show that the moduli space of U⊕⟨−2k⟩-polarized K3 surfaces is unirational for k≤50 and k∉{11,35,42,48}, and for other several values of k up to k=97. Our proof is based on a systematic study of the projective models of elliptic K3 surfaces in Pn for 3≤n≤5 containing either the union of two rational curves or the union of a rational and an elliptic curve intersecting at one point.

UR - http://www.scopus.com/inward/record.url?scp=85145694487&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2008.12077

DO - 10.48550/arXiv.2008.12077

M3 - Article

VL - 173

SP - 405

EP - 423

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1-2

ER -