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Niveau: Supérieur, Doctorat, Bac+8

ar X iv :1 10 4. 28 86 v1 [ ma th. AG ] 14 A pr 20 11 Prym varieties and their moduli Gavril Farkas 1. Prym, Schottky and 19th century theta functions Prym varieties are principally polarized abelian varieties associated to etale double covers of curves. They establish a bridge between the geometry of curves and that of abelian varieties and as such, have been studied for over 100 years, initially from an analytic [Wi], [SJ], [HFR] and later from an algebraic [M] point of view. Several approaches to the Schottky problem are centered around Prym varieties, see [B1], [D2] and references therein. In 1909, in an attempt to characterize genus g theta functions coming from Riemann surfaces and thus solve what is nowadays called the Schottky problem, F. Schottky and H. Jung, following earlier work of Wirtinger, associated to certain two-valued Prym differentials on a Riemann surface C new theta constants which then they related to the classical theta constants, establishing what came to be known as the Scottky-Jung relations. The first rigorous proof of the Schottky-Jung relations has been given by H. Farkas [HF]. The very definition of these differentials forces one to consider the parameter space of unramified double covers of curves of genus g.

- dissertation

ar X iv :1 10 4. 28 86 v1 [ ma th. AG ] 14 A pr 20 11 Prym varieties and their moduli Gavril Farkas 1. Prym, Schottky and 19th century theta functions Prym varieties are principally polarized abelian varieties associated to etale double covers of curves. They establish a bridge between the geometry of curves and that of abelian varieties and as such, have been studied for over 100 years, initially from an analytic [Wi], [SJ], [HFR] and later from an algebraic [M] point of view. Several approaches to the Schottky problem are centered around Prym varieties, see [B1], [D2] and references therein. In 1909, in an attempt to characterize genus g theta functions coming from Riemann surfaces and thus solve what is nowadays called the Schottky problem, F. Schottky and H. Jung, following earlier work of Wirtinger, associated to certain two-valued Prym differentials on a Riemann surface C new theta constants which then they related to the classical theta constants, establishing what came to be known as the Scottky-Jung relations. The first rigorous proof of the Schottky-Jung relations has been given by H. Farkas [HF]. The very definition of these differentials forces one to consider the parameter space of unramified double covers of curves of genus g.

- necessarily multi-sheeted
- multi-valued complex
- double cover
- holomorphic function
- theta functions
- constants ?
- prym's papers
- complex functions
- riemann's dissertation
- berlin until his

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Published by | profil-feym-2012 |

Reads | 41 |

Language | English |

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