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2014 K3 surfaces and equations for Hilbert modular surfaces
Noam Elkies, Abhinav Kumar
Algebra Number Theory 8(10): 2297-2411 (2014). DOI: 10.2140/ant.2014.8.2297

Abstract

We outline a method to compute rational models for the Hilbert modular surfaces Y(D), which are coarse moduli spaces for principally polarized abelian surfaces with real multiplication by the ring of integers in (D), via moduli spaces of elliptic K3 surfaces with a Shioda–Inose structure. In particular, we compute equations for all thirty fundamental discriminants D with 1<D<100, and analyze rational points and curves on these Hilbert modular surfaces, producing examples of genus-2 curves over  whose Jacobians have real multiplication over .

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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

Information

Received: 22 January 2013; Revised: 26 August 2013; Accepted: 28 October 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1317.11048
MathSciNet: MR3298543
Digital Object Identifier: 10.2140/ant.2014.8.2297

Subjects:
Primary: 11F41
Secondary: 14G35, 14J27, 14J28

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.8 • No. 10 • 2014
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