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arXiv · 1504.07498

Icosahedral invariants and Shimura curves

Atsuhira Nagano
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Abstract

Shimura curves are moduli spaces of abelian surfaces with quaternion multiplication. Models of Shimura curves are very important in number theory. Klein's icosahedral invariants $\mathfrak{A},\mathfrak{B}$ and $\mathfrak{C}$ give the Hilbert modular forms for $\sqrt{5}$ via the period mapping for a family of $K3$ surfaces. Using the period mappings for several families of $K3$ surfaces, we obtain explicit models of Shimura curves with small discriminant in the weighted projective space ${\rm Proj} (\mathbb{C}[\mathfrak{A},\mathfrak{B},\mathfrak{C}])$.

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Atsuhira Nagano. 2016-08-07. Icosahedral invariants and Shimura curves. https://doi.org/10.5802/jtnb.993

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