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Prym varieties of triple coverings

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Classical Prym varieties are principally polarised abelian varieties associated to etale double coverings of curves. We study a special class of Prym-Tjurin varieties of exponent 3, coming from non-cyclic etale triple coverings of curves of genus 2. We show that the moduli space of such coverings is a rational threefold, mapping 10:1 via the Prym map to the moduli space of principally polarised abelian surfaces. The crucial ingredient used to obtain such an explicit description of the moduli space is that any genus 4 curve which is a non-cyclic triple cover of a genus 2 curve is actually hyperelliptic. We also describe the extended Prym map from the moduli space of admissible S_3-covers onto A_2. This is a joint work with Herbert Lange.

This talk is part of the Algebraic Geometry Seminar series.

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