TY - JOUR

T1 - Two moduli spaces of abelian fourfolds with an automorphism of order five

AU - Van Geemen, Bert

AU - Schütt, Matthias

PY - 2012/10

Y1 - 2012/10

N2 - We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarized abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical model in P 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

AB - We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarized abelian fourfolds with an automorphism of order five. The surface has a 24-nodal canonical model in P 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

KW - abelian fourfold

KW - automorphism

KW - Hilbert modular surface

KW - Moduli space

KW - Shimura variety

KW - zeta function

UR - http://www.scopus.com/inward/record.url?scp=84869439316&partnerID=8YFLogxK

U2 - 10.1142/S0129167X1250108X

DO - 10.1142/S0129167X1250108X

M3 - Article

AN - SCOPUS:84869439316

VL - 23

JO - International Journal of Mathematics

JF - International Journal of Mathematics

SN - 0129-167X

IS - 10

M1 - 1250108

ER -