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SUMMARY:Prym varieties of triple coverings - Angela Ortega (Humboldt\, Ber
 lin)
DTSTART:20110324T140000Z
DTEND:20110324T150000Z
UID:TALK29947@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:Classical Prym varieties are principally polarised abelian var
 ieties\nassociated to etale double coverings of curves. We study a special
 \nclass of Prym-Tjurin varieties of exponent 3\, coming from non-cyclic\ne
 tale triple coverings of curves of genus 2. We show that the moduli\nspace
  of such coverings is a rational threefold\, mapping 10:1 via the\nPrym ma
 p to the moduli space of principally polarised abelian surfaces.\nThe cruc
 ial ingredient used to obtain such an explicit description of\nthe moduli 
 space is that any genus 4 curve which is a non-cyclic triple\ncover of a g
 enus 2 curve is actually hyperelliptic.\nWe also describe the extended Pry
 m map from the moduli space of *admissible*\nS_3-covers onto A_2. This is 
 a joint work with Herbert Lange.
LOCATION:Isaac Newton Institute\, Cambridge
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