Abstract
We outline a method to compute rational models for the Hilbert modular surfaces , which are coarse moduli spaces for principally polarized abelian surfaces with real multiplication by the ring of integers in , via moduli spaces of elliptic K3 surfaces with a Shioda–Inose structure. In particular, we compute equations for all thirty fundamental discriminants with , and analyze rational points and curves on these Hilbert modular surfaces, producing examples of genus- curves over whose Jacobians have real multiplication over .
Citation
Noam Elkies. Abhinav Kumar. "K3 surfaces and equations for Hilbert modular surfaces." Algebra Number Theory 8 (10) 2297 - 2411, 2014. https://doi.org/10.2140/ant.2014.8.2297
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