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

Institut für Algebraische Geometrie

Stony Brook University (SBU)

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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.

Originalsprache	Englisch
Seiten (von - bis)	657-703
Seitenumfang	47
Fachzeitschrift	Moscow mathematical journal
Jahrgang	22
Ausgabenummer	4
DOIs	https://doi.org/10.17323/1609-4514-2022-22-4-657-703
Publikationsstatus	Veröffentlicht - Okt. 2022

ASJC Scopus Sachgebiete

Allgemeine Mathematik

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

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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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author = "Samuel Grushevsky and Klaus Hulek",

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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.

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KW - effective cycles

KW - extremal rays

KW - Moduli spaces

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