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

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

2010-10-19

arxiv.org/abs/1010.3897v1

Mathematics

Algebraic Geometry

27 pages

Scientific paper

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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