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SUMMARY:Giusi Capobianco (Roma Tor Vergata)
DTSTART:20250117T133000Z
DTEND:20250117T143000Z
DTSTAMP:20260422T172351Z
UID:TGiZ/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TGiZ/64/">Th
 e tropical 1-fold Abel-Prym map</a>\nby Giusi Capobianco (Roma Tor Vergata
 ) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n\n\nAbstract\nThe
  algebraic Abel-Prym map relates the geometry of a double cover of algebra
 ic curves with their corresponding Prym varieties. Birkenhake and Lange pr
 oved that the map has degree 2 if and only if the cover curve is hyperelli
 ptic.\nIn the talk I will present joint work with Yoav Len\, in which we i
 nvestigate the 1-fold Abel-Prym map in the tropical setting and prove simi
 lar results. I will describe a new combinatorial construction of hyperelli
 ptic double covers of metric graphs and prove that the tropical Abel-Prym 
 map is a harmonic morphism of degree 2.  Furthermore\, we will see that th
 e Jacobian of the image of this map is isomorphic\, as pptav\, to the Prym
  variety of the cover. When the double cover is not hyperelliptic however\
 , contrary to the algebraic result\, the tropical Abel-Prym map is almost 
 never injective. I will provide counterexamples and discuss its image.\n
LOCATION:https://researchseminars.org/talk/TGiZ/64/
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