What is the principally polarized abelian variety of dimension six?
 
Gavril Farkas (Humboldt University, Berlin)



The general principally polarized abelian variety of dimension at most five is known to be a Prym variety. This reduces the study of abelian varieties of small dimension to the beautifully concrete theory of algebraic curves. I will discuss recent progress on finding a structure theorem for principally polarized abelian varieties of dimension six, and the implications this uniformization result has on the geometry of their moduli space.



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