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Global Prym-Torelli theorem for double coverings of elliptic curves

Hold Date
2019-11-01 16:00〜2019-11-01 17:00
Lecture Room M W1-C-513, West Zone 1, Ito campus, Kyushu University
Object person
researchers and graduate students 
Atsushi IKEDA (Tokyo Denki University)

Prym variety is a polarized abelian variety constructed from a double covering of a nonsingular projective curve. The construction defines the Prym map from the moduli space of coverings to the moduli space of polarized abelian varieties. We discuss the injectivity of the Prym maps under a suitable condition on the dimension of the moduli spaces. It is known that the Prym map is generically injective, but it is not injective in general. In this talk, we state that the Prym maps are injective for double coverings of elliptic curves, and explain how the covering is reconstructed from the polarized abelian variety.

* This seminar is combined with Algebra Seminar.