Details
| Original language | English |
|---|---|
| Pages (from-to) | 657-703 |
| Number of pages | 47 |
| Journal | Moscow mathematical journal |
| Volume | 22 |
| Issue number | 4 |
| Publication status | Published - Oct 2022 |
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.
Keywords
- abelian varieties, effective cycles, extremal rays, Moduli spaces
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Moscow mathematical journal, Vol. 22, No. 4, 10.2022, p. 657-703.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - On the Cone of Effective Surfaces on A3
AU - Grushevsky, Samuel
AU - Hulek, Klaus
N1 - Funding Information: Research of the first named author is supported in part by the National Science Foundation under the grant DMS-18-02116. Research of the second named author is supported in part by DFG grant Hu-337/7-1.
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 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 - http://www.scopus.com/inward/record.url?scp=85141769570&partnerID=8YFLogxK
U2 - 10.17323/1609-4514-2022-22-4-657-703
DO - 10.17323/1609-4514-2022-22-4-657-703
M3 - Article
AN - SCOPUS:85141769570
VL - 22
SP - 657
EP - 703
JO - Moscow mathematical journal
JF - Moscow mathematical journal
SN - 1609-3321
IS - 4
ER -