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

authored by

Klaus Hulek, Samuel Grushevsky

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)

Institut für Algebraische Geometrie

External Organisation(s)

Stony Brook University (SBU)

Type

Artikel

Journal

Moscow Mathematical Journal

Volume

22

Pages

657-703

ISSN

1609-3321

Publication date

10.2022

Publication status

Veröffentlicht

Peer reviewed

Yes

Electronic version(s)

https://arxiv.org/abs/2007.02995 (Access: Offen)
http://www.mathjournals.org/mmj/2022-022-004/2022-022-004-004.html (Access: Geschlossen)