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On the cone of effective surfaces on $\overline{\mathcal A}_3$

authored by
Samuel Grushevsky, Klaus Hulek
Abstract

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 $g\ge 3$, we further conjecture that they generate the cone of effective surfaces on the perfect cone toroidal compactification of ${\mathcal A}_g$ for any $g\ge 3$.

Organisation(s)
Institute of Algebraic Geometry
Riemann Center for Geometry and Physics
Type
Preprint
Publication date
06.07.2020
Publication status