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Register a new userOn the cone of effective surfaces on $overline{mathcal A}_3$
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We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification $overline{mathcal A}_3$ of the moduli space ${mathcal A}_3$ of complex principally polarized abelian threefolds, and we conjecture that the cone of effective surfaces is generated by these surfaces. As the surfaces we define can be defined in any genus $gge 3$, we further conjecture that they generate the cone of effective surfaces on the perfect cone toroidal compactification of ${mathcal A}_g$ for any $gge 3$.
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