TY - JOUR
T1 - Shimura curves as intersections of humbert surfaces and defining equations of QM-curves of genus two
AU - Hashimoto, Ki Ichiro
AU - Murabayashi, Naoki
PY - 1995/6
Y1 - 1995/6
N2 - Shimura curves classify isomorphism classes of abelian surfaces with quaternion multiplication. In this paper, we are concerned with a fibre space, the base space of which is a Shimura curve and fibres are curves of genus two whose jacobian varieties are abelian surfaces of the above type. We shall give an explicit defining equation for such a fibre space when the discriminant of the quaternion algebra is 6 or 10.
AB - Shimura curves classify isomorphism classes of abelian surfaces with quaternion multiplication. In this paper, we are concerned with a fibre space, the base space of which is a Shimura curve and fibres are curves of genus two whose jacobian varieties are abelian surfaces of the above type. We shall give an explicit defining equation for such a fibre space when the discriminant of the quaternion algebra is 6 or 10.
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U2 - 10.2748/tmj/1178225596
DO - 10.2748/tmj/1178225596
M3 - Article
AN - SCOPUS:84972546471
SN - 0040-8735
VL - 47
SP - 271
EP - 296
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
IS - 2
ER -