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Generic vanishing subschemes of codimension three
We classify geometrically nondegenerate GV subschemes of codimension three in indecomposable principally polarized complex abelian varieties of dimension $g\ge6$. Every such subscheme is a translate of $\pm W_{g-3}(C)$ in the Jacobian of a smooth curve $C$. The proof studies the theta-dual surface:
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