TY - JOUR

T1 - On the cone of effective surfaces on \(\overline{\mathcal A}_3\)

AU - Hulek, Klaus

AU - Grushevsky, Samuel

PY - 2022/10

Y1 - 2022/10

N2 - 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 \(g\ge 3\).

AB - 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 \(g\ge 3\).

KW - math.AG

M3 - Article

VL - 22

SP - 657

EP - 703

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

SN - 1609-3321

IS - 4

ER -