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.

Two moduli spaces of abelian fourfolds with an automorphism of order five / B. van Geemen, M. Schuett. - In: INTERNATIONAL JOURNAL OF MATHEMATICS. - ISSN 0129-167X. - 23:10(2012 Oct), pp. 1250108.1-1250108.31. [10.1142/S0129167X1250108X]

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

B. van Geemen;
2012-10

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.
abelian fourfold; automorphism; Hilbert modular surface; Moduli space; Shimura variety; zeta function
Settore MAT/03 - Geometria
INTERNATIONAL JOURNAL OF MATHEMATICS
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/213953
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