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arXiv · 1010.3897

Two moduli spaces of abelian fourfolds with an automorphism of order five

Bert van Geemen·Matthias Schuett
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Abstract

We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarised abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical model in IP^4 which is the complete intersection of two S_5-invariant cubics. It is dominated by a Hilbert modular surface and we give a modular interpretation for this. We also determine the L-series of these varieties as well as those of several modular covers of the Shimura curve.

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Bert van Geemen, Matthias Schuett. 2010-10-19. Two moduli spaces of abelian fourfolds with an automorphism of order five. https://arxiv.org/abs/1010.3897

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