### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 271-296 |

Number of pages | 26 |

Journal | Tohoku Mathematical Journal |

Volume | 47 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1995 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Tohoku Mathematical Journal*,

*47*(2), 271-296. https://doi.org/10.2748/tmj/euclid.tmj.1178225596

**Shimura curves as intersections of humbert surfaces and defining equations of QM-curves of genus two.** / Hashimoto, Kiichiro; Murabayashi, Naoki.

Research output: Contribution to journal › Article

*Tohoku Mathematical Journal*, vol. 47, no. 2, pp. 271-296. https://doi.org/10.2748/tmj/euclid.tmj.1178225596

}

TY - JOUR

T1 - Shimura curves as intersections of humbert surfaces and defining equations of QM-curves of genus two

AU - Hashimoto, Kiichiro

AU - Murabayashi, Naoki

PY - 1995

Y1 - 1995

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.

UR - http://www.scopus.com/inward/record.url?scp=84972546471&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972546471&partnerID=8YFLogxK

U2 - 10.2748/tmj/euclid.tmj.1178225596

DO - 10.2748/tmj/euclid.tmj.1178225596

M3 - Article

AN - SCOPUS:84972546471

VL - 47

SP - 271

EP - 296

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 2

ER -