Abstract
We give a construction of singular K3 surfaces with discriminant 3 and 4 as double coverings over the projective plane. Focusing on the similarities in their branching loci, we can generalize this construction, and obtain a three dimensional moduli space of certain K3 surfaces which admit infinite automorphism groups. Moreover, we show that these K3 surfaces are characterized in terms of the configuration of the singular fibres of a jacobian elliptic fibration and also in terms of periods.
Acknowledgment
The author would like to thank his advisor Fumiharu Kato for many helpful conversations and advices. He would also like to thank Professor Shigeyuki Kondo for very useful discussions. Last but not least, I would like to thank the referee for the valuable comments, which greatly improved the content of this paper.
Citation
Taiki Takatsu. "On the geometry of singular K3 surfaces with discriminant 3, 4 and 7." Kodai Math. J. 45 (1) 157 - 173, March 2022. https://doi.org/10.2996/kmj/kmj45110
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