ON THE CONE OF EFFECTIVE SURFACES ON A3

Samuel Grushevsky; Klaus Hulek

doi:10.17323/1609-4514-2022-22-4-657-703

ON THE CONE OF EFFECTIVE SURFACES ON A₃

Samuel Grushevsky
, Klaus Hulek

Simons Center for Geometry & Physics

Leibniz University Hannover

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

1 Scopus citations

Abstract

We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification A₃ of the moduli space A₃ 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 ≥ 3, we further conjecture that they generate the cone of effective surfaces on the perfect cone compactification A^Perf g for any g ≥ 3.

Original language	English
Pages (from-to)	657-703
Number of pages	47
Journal	Moscow Mathematical Journal
Volume	22
Issue number	4
DOIs	https://doi.org/10.17323/1609-4514-2022-22-4-657-703
State	Published - Oct 1 2022

Keywords

abelian varieties
effective cycles
extremal rays
Moduli spaces

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abstract = "We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification A3 of the moduli space A3 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 ≥ 3, we further conjecture that they generate the cone of effective surfaces on the perfect cone compactification APerf g for any g ≥ 3.",

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N2 - We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification A3 of the moduli space A3 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 ≥ 3, we further conjecture that they generate the cone of effective surfaces on the perfect cone compactification APerf g for any g ≥ 3.

AB - We determine five extremal effective rays of the four-dimensional cone of effective surfaces on the toroidal compactification A3 of the moduli space A3 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 ≥ 3, we further conjecture that they generate the cone of effective surfaces on the perfect cone compactification APerf g for any g ≥ 3.

KW - abelian varieties

KW - effective cycles

KW - extremal rays

KW - Moduli spaces

UR - https://www.scopus.com/pages/publications/85141769570

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JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 4

ER -

ON THE CONE OF EFFECTIVE SURFACES ON A₃

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Keywords

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