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Showing 1 to 2 of 2 for “"Hilbert modular surfaces"”.
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Low Genus Curves on Compact Shimura Surfaces
… complex curves on two types of compact Shimura surfaces: compact variants of Picard and Hilbert modular surfaces. For the compact variant of Picard modular surfaces, we prove there are no curves of a fixed genus when the defining discriminant is sufficiently large. For the compact variant of …
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Explicit moduli spaces for curves of genus 1 and 2
… modules. In particular, we study the moduli surfaces $Z_{N,r}$ which parametrise $N$-congruences of elliptic curves which raise the Weil pairing to a power of $r$. We first study the birational geometry of the surfaces $Z_{N,r}^{\text{sym}}$ which arise as quotients of the surfaces $Z_{N,r}$ …