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

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Klaus Hulek
  • Samuel Grushevsky

Research Organisations

External Research Organisations

  • Stony Brook University (SBU)

Details

Original languageEnglish
Pages (from-to)657-703
JournalMoscow Mathematical Journal
Volume22
Issue number4
Publication statusPublished - Oct 2022

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 \(g\ge 3\).

Keywords

    math.AG

Cite this

On the cone of effective surfaces on \(\overline{\mathcal A}_3\). / Hulek, Klaus; Grushevsky, Samuel.
In: Moscow Mathematical Journal, Vol. 22, No. 4, 10.2022, p. 657-703.

Research output: Contribution to journal › Article › Research › peer review

Hulek, Klaus ; Grushevsky, Samuel. / On the cone of effective surfaces on \(\overline{\mathcal A}_3\). In: Moscow Mathematical Journal. 2022 ; Vol. 22, No. 4. pp. 657-703.
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